| # |
ODE |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=6 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.358 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 y\\ y^{\prime }&=2 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=10 y\\ y^{\prime }&=-10 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {y}{2}\\ y^{\prime }&=-8 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=8 y\\ y^{\prime }&=-2 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=6 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=10 x-7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=13 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-9 x+6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.307 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 10 x_{1}^{\prime }&=-x_{1}+x_{3}\\ 10 x_{2}^{\prime }&=x_{1}-x_{2}\\ 10 x_{3}^{\prime }&=x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+3 y\\ y^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.291 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=2 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+2 y\\ y^{\prime }&=-3 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y\\ y^{\prime }&=5 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x-4 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+9 y\\ y^{\prime }&=-2 x-5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+y+2 t\\ y^{\prime }&=-2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=x+2 y-{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-3 y+2 \sin \left (2 t \right )\\ y^{\prime }&=x-2 y-\cos \left (2 t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 y^{\prime }&=4 x+5 y\\ 2 x^{\prime }-y^{\prime }&=3 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -x^{\prime }+2 y^{\prime }&=x+3 y+{\mathrm e}^{t}\\ 3 x^{\prime }-4 y^{\prime }&=x-15 y+{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y+z\\ y^{\prime }&=6 x-y\\ z^{\prime }&=-x-2 y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=-4 x+4 y-2 z\\ z^{\prime }&=-4 y+4 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
64.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+z+{\mathrm e}^{-t}\\ y^{\prime }&=x+z\\ z^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 y\\ y^{\prime }&=3 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t}\\ y^{\prime }&=5 x-y-t^{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.359 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=t x-{\mathrm e}^{t} y+\cos \left (t \right )\\ y^{\prime }&={\mathrm e}^{-t} x+t^{2} y-\sin \left (t \right )\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+z\\ y^{\prime }&=x+z\\ z^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-3 y\\ y^{\prime }&=x+y+2 z\\ z^{\prime }&=5 y-7 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
11.829 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-4 y+z+t\\ y^{\prime }&=x-3 z+t^{2}\\ z^{\prime }&=6 y-7 z+t^{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
109.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=t x-y+{\mathrm e}^{t} z\\ y^{\prime }&=2 x+t^{2} y-z\\ z^{\prime }&={\mathrm e}^{-t} x+3 t y+t^{3} z\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=2 x_{3}\\ x_{3}^{\prime }&=3 x_{4}\\ x_{4}^{\prime }&=4 x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.947 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}+x_{3}+1\\ x_{2}^{\prime }&=x_{3}+x_{4}+t\\ x_{3}^{\prime }&=x_{1}+x_{4}+t^{2}\\ x_{4}^{\prime }&=x_{1}+x_{2}+t^{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.263 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+2 x_{2}\\ x_{2}^{\prime }&=-3 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+2 x_{2}\\ x_{2}^{\prime }&=-3 x_{1}+4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.376 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-x_{2}\\ x_{2}^{\prime }&=5 x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}\\ x_{2}^{\prime }&=-2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-3 x_{2}\\ x_{2}^{\prime }&=6 x_{1}-7 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=-x_{1}+3 x_{2}-2 x_{3}\\ x_{3}^{\prime }&=-x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{3}\\ x_{3}^{\prime }&=x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}+x_{3}\\ x_{2}^{\prime }&=6 x_{1}-x_{2}\\ x_{3}^{\prime }&=-x_{1}-2 x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.656 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-8 x_{1}-11 x_{2}-2 x_{3}\\ x_{2}^{\prime }&=6 x_{1}+9 x_{2}+2 x_{3}\\ x_{3}^{\prime }&=-6 x_{1}-6 x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4}\\ x_{2}^{\prime }&=x_{2}\\ x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4}\\ x_{4}^{\prime }&=-4 x_{2}-x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+3 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+4 x_{2}\\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}\\ x_{2}^{\prime }&=6 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=6 x_{1}-7 x_{2}\\ x_{2}^{\prime }&=x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=9 x_{1}+5 x_{2}\\ x_{2}^{\prime }&=-6 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+4 x_{2}\\ x_{2}^{\prime }&=6 x_{1}-5 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.384 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-5 x_{2}\\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=9 x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-9 x_{2}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-4 x_{2}\\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.387 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=7 x_{1}-5 x_{2}\\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-50 x_{1}+20 x_{2}\\ x_{2}^{\prime }&=100 x_{1}-60 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3}\\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3}\\ x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3}\\ x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}+4 x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{1}+x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}+x_{2}+3 x_{3}\\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3}\\ x_{3}^{\prime }&=3 x_{1}+x_{2}+5 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-6 x_{3}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3}\\ x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=-5 x_{1}-4 x_{2}-2 x_{3}\\ x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3}\\ x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{2}^{\prime }&=-4 x_{1}-3 x_{2}-x_{3}\\ x_{3}^{\prime }&=4 x_{1}+4 x_{2}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3}\\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.900 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+x_{3}\\ x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3}\\ x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=2 x_{1}+2 x_{2}\\ x_{3}^{\prime }&=3 x_{2}+3 x_{3}\\ x_{4}^{\prime }&=4 x_{3}+4 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+9 x_{4}\\ x_{2}^{\prime }&=4 x_{1}+2 x_{2}-10 x_{4}\\ x_{3}^{\prime }&=-x_{3}+8 x_{4}\\ x_{4}^{\prime }&=x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}\\ x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4}\\ x_{3}^{\prime }&=5 x_{3}\\ x_{4}^{\prime }&=-21 x_{3}-2 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.155 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4}\\ x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4}\\ x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4}\\ x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.148 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 y\\ y^{\prime }&=3 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.506 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t}\\ y^{\prime }&=5 x-y-t^{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.329 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+z\\ y^{\prime }&=x+z\\ z^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=2 x_{3}\\ x_{3}^{\prime }&=3 x_{4}\\ x_{4}^{\prime }&=4 x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.155 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}+x_{3}+1\\ x_{2}^{\prime }&=x_{3}+x_{4}+t\\ x_{3}^{\prime }&=x_{1}+x_{4}+t^{2}\\ x_{4}^{\prime }&=x_{1}+x_{2}+t^{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.739 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=6 x_{1}\\ x_{2}^{\prime }&=-3 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+2 x_{2}\\ x_{2}^{\prime }&=-3 x_{1}+4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+3 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+4 x_{2}\\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.593 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}\\ x_{2}^{\prime }&=6 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=6 x_{1}-7 x_{2}\\ x_{2}^{\prime }&=x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=9 x_{1}+5 x_{2}\\ x_{2}^{\prime }&=-6 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+4 x_{2}\\ x_{2}^{\prime }&=6 x_{1}-5 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.642 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-5 x_{2}\\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=9 x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-9 x_{2}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.905 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-4 x_{2}\\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=7 x_{1}-5 x_{2}\\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.876 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-50 x_{1}+20 x_{2}\\ x_{2}^{\prime }&=100 x_{1}-60 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3}\\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3}\\ x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.981 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3}\\ x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}+4 x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{1}+x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}+x_{2}+3 x_{3}\\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3}\\ x_{3}^{\prime }&=3 x_{1}+x_{2}+5 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-6 x_{3}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3}\\ x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=-5 x_{1}-4 x_{2}-2 x_{3}\\ x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3}\\ x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{2}^{\prime }&=-4 x_{1}-3 x_{2}-x_{3}\\ x_{3}^{\prime }&=4 x_{1}+4 x_{2}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3}\\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.349 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+x_{3}\\ x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3}\\ x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.804 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=2 x_{1}+2 x_{2}\\ x_{3}^{\prime }&=3 x_{2}+3 x_{3}\\ x_{4}^{\prime }&=4 x_{3}+4 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.463 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+9 x_{4}\\ x_{2}^{\prime }&=4 x_{1}+2 x_{2}-10 x_{4}\\ x_{3}^{\prime }&=-x_{3}+8 x_{4}\\ x_{4}^{\prime }&=x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.657 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}\\ x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4}\\ x_{3}^{\prime }&=5 x_{3}\\ x_{4}^{\prime }&=-21 x_{3}-2 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.868 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4}\\ x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4}\\ x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4}\\ x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.710 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-40 x_{1}-12 x_{2}+54 x_{3}\\ x_{2}^{\prime }&=35 x_{1}+13 x_{2}-46 x_{3}\\ x_{3}^{\prime }&=-25 x_{1}-7 x_{2}+34 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-20 x_{1}+11 x_{2}+13 x_{3}\\ x_{2}^{\prime }&=12 x_{1}-x_{2}-7 x_{3}\\ x_{3}^{\prime }&=-48 x_{1}+21 x_{2}+31 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.290 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=147 x_{1}+23 x_{2}-202 x_{3}\\ x_{2}^{\prime }&=-90 x_{1}-9 x_{2}+129 x_{3}\\ x_{3}^{\prime }&=90 x_{1}+15 x_{2}-123 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.226 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=9 x_{1}-7 x_{2}-5 x_{3}\\ x_{2}^{\prime }&=-12 x_{1}+7 x_{2}+11 x_{3}+9 x_{4}\\ x_{3}^{\prime }&=24 x_{1}-17 x_{2}-19 x_{3}-9 x_{4}\\ x_{4}^{\prime }&=-18 x_{1}+13 x_{2}+17 x_{3}+9 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.849 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=13 x_{1}-42 x_{2}+106 x_{3}+139 x_{4}\\ x_{2}^{\prime }&=2 x_{1}-16 x_{2}+52 x_{3}+70 x_{4}\\ x_{3}^{\prime }&=x_{1}+6 x_{2}-20 x_{3}-31 x_{4}\\ x_{4}^{\prime }&=-x_{1}-6 x_{2}+22 x_{3}+33 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.496 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=23 x_{1}-18 x_{2}-16 x_{3}\\ x_{2}^{\prime }&=-8 x_{1}+6 x_{2}+7 x_{3}+9 x_{4}\\ x_{3}^{\prime }&=34 x_{1}-27 x_{2}-26 x_{3}-9 x_{4}\\ x_{4}^{\prime }&=-26 x_{1}+21 x_{2}+25 x_{3}+12 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.062 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=47 x_{1}-8 x_{2}+5 x_{3}-5 x_{4}\\ x_{2}^{\prime }&=-10 x_{1}+32 x_{2}+18 x_{3}-2 x_{4}\\ x_{3}^{\prime }&=139 x_{1}-40 x_{2}-167 x_{3}-121 x_{4}\\ x_{4}^{\prime }&=-232 x_{1}+64 x_{2}+360 x_{3}+248 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.475 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=139 x_{1}-14 x_{2}-52 x_{3}-14 x_{4}+28 x_{5}\\ x_{2}^{\prime }&=-22 x_{1}+5 x_{2}+7 x_{3}+8 x_{4}-7 x_{5}\\ x_{3}^{\prime }&=370 x_{1}-38 x_{2}-139 x_{3}-38 x_{4}+76 x_{5}\\ x_{4}^{\prime }&=152 x_{1}-16 x_{2}-59 x_{3}-13 x_{4}+35 x_{5}\\ x_{5}^{\prime }&=95 x_{1}-10 x_{2}-38 x_{3}-7 x_{4}+23 x_{5}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
11.388 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=9 x_{1}+13 x_{2}-13 x_{6}\\ x_{2}^{\prime }&=-14 x_{1}+19 x_{2}-10 x_{3}-20 x_{4}+10 x_{5}+4 x_{6}\\ x_{3}^{\prime }&=-30 x_{1}+12 x_{2}-7 x_{3}-30 x_{4}+12 x_{5}+18 x_{6}\\ x_{4}^{\prime }&=-12 x_{1}+10 x_{2}-10 x_{3}-9 x_{4}+10 x_{5}+2 x_{6}\\ x_{5}^{\prime }&=6 x_{1}+9 x_{2}+6 x_{4}+5 x_{5}-15 x_{6}\\ x_{6}^{\prime }&=-14 x_{1}+23 x_{2}-10 x_{3}-20 x_{4}+10 x_{5}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
9.240 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=9 x_{1}+4 x_{2}\\ x_{2}^{\prime }&=-6 x_{1}-x_{2}\\ x_{3}^{\prime }&=6 x_{1}+4 x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.878 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-3 x_{2}\\ x_{2}^{\prime }&=3 x_{1}+7 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.503 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}+2 x_{3}\\ x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-7 x_{3}\\ x_{3}^{\prime }&=x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{3}\\ x_{2}^{\prime }&=x_{4}\\ x_{3}^{\prime }&=-2 x_{1}+2 x_{2}-3 x_{3}+x_{4}\\ x_{4}^{\prime }&=2 x_{1}-2 x_{2}+x_{3}-3 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.369 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+x_{2}\\ x_{2}^{\prime }&=-x_{1}-4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.498 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-x_{2}\\ x_{2}^{\prime }&=x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+5 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-x_{2}\\ x_{2}^{\prime }&=x_{1}+5 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.305 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=7 x_{1}+x_{2}\\ x_{2}^{\prime }&=-4 x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-4 x_{2}\\ x_{2}^{\prime }&=4 x_{1}+9 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.501 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}\\ x_{2}^{\prime }&=-7 x_{1}+9 x_{2}+7 x_{3}\\ x_{3}^{\prime }&=2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=25 x_{1}+12 x_{2}\\ x_{2}^{\prime }&=-18 x_{1}-5 x_{2}\\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+13 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.930 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-19 x_{1}+12 x_{2}+84 x_{3}\\ x_{2}^{\prime }&=5 x_{2}\\ x_{3}^{\prime }&=-8 x_{1}+4 x_{2}+33 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.959 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-13 x_{1}+40 x_{2}-48 x_{3}\\ x_{2}^{\prime }&=-8 x_{1}+23 x_{2}-24 x_{3}\\ x_{3}^{\prime }&=3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}-4 x_{3}\\ x_{2}^{\prime }&=-x_{1}-x_{2}-x_{3}\\ x_{3}^{\prime }&=x_{1}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+x_{3}\\ x_{2}^{\prime }&=-x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{1}-x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+x_{3}\\ x_{2}^{\prime }&=x_{2}-4 x_{3}\\ x_{3}^{\prime }&=x_{2}-3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{3}\\ x_{2}^{\prime }&=-5 x_{1}-x_{2}-5 x_{3}\\ x_{3}^{\prime }&=4 x_{1}+x_{2}-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}-9 x_{2}\\ x_{2}^{\prime }&=x_{1}+4 x_{2}\\ x_{3}^{\prime }&=x_{1}+3 x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.888 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2}-3 x_{3}\\ x_{3}^{\prime }&=2 x_{1}+3 x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=18 x_{1}+7 x_{2}+4 x_{3}\\ x_{3}^{\prime }&=-27 x_{1}-9 x_{2}-5 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}+x_{3}\\ x_{3}^{\prime }&=-2 x_{1}-4 x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.795 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4}\\ x_{2}^{\prime }&=x_{2}\\ x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4}\\ x_{4}^{\prime }&=-4 x_{2}-x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}+x_{4}\\ x_{2}^{\prime }&=2 x_{2}+x_{3}\\ x_{3}^{\prime }&=2 x_{3}+x_{4}\\ x_{4}^{\prime }&=2 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.027 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-4 x_{2}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}\\ x_{3}^{\prime }&=x_{1}+2 x_{2}+x_{3}\\ x_{4}^{\prime }&=x_{2}+x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+3 x_{2}+7 x_{3}\\ x_{2}^{\prime }&=-x_{2}-4 x_{3}\\ x_{3}^{\prime }&=x_{2}+3 x_{3}\\ x_{4}^{\prime }&=-6 x_{2}-14 x_{3}+x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.966 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=39 x_{1}+8 x_{2}-16 x_{3}\\ x_{2}^{\prime }&=-36 x_{1}-5 x_{2}+16 x_{3}\\ x_{3}^{\prime }&=72 x_{1}+16 x_{2}-29 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.036 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=28 x_{1}+50 x_{2}+100 x_{3}\\ x_{2}^{\prime }&=15 x_{1}+33 x_{2}+60 x_{3}\\ x_{3}^{\prime }&=-15 x_{1}-30 x_{2}-57 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+17 x_{2}+4 x_{3}\\ x_{2}^{\prime }&=-x_{1}+6 x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{2}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}\\ x_{3}^{\prime }&=-3 x_{1}+2 x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+5 x_{2}-5 x_{3}\\ x_{2}^{\prime }&=3 x_{1}-x_{2}+3 x_{3}\\ x_{3}^{\prime }&=8 x_{1}-8 x_{2}+10 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-15 x_{1}-7 x_{2}+4 x_{3}\\ x_{2}^{\prime }&=34 x_{1}+16 x_{2}-11 x_{3}\\ x_{3}^{\prime }&=17 x_{1}+7 x_{2}+5 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+x_{2}+x_{3}-2 x_{4}\\ x_{2}^{\prime }&=7 x_{1}-4 x_{2}-6 x_{3}+11 x_{4}\\ x_{3}^{\prime }&=5 x_{1}-x_{2}+x_{3}+3 x_{4}\\ x_{4}^{\prime }&=6 x_{1}-2 x_{2}-2 x_{3}+6 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.878 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}-2 x_{3}+x_{4}\\ x_{2}^{\prime }&=3 x_{2}-5 x_{3}+3 x_{4}\\ x_{3}^{\prime }&=-13 x_{2}+22 x_{3}-12 x_{4}\\ x_{4}^{\prime }&=-27 x_{2}+45 x_{3}-25 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.816 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=35 x_{1}-12 x_{2}+4 x_{3}+30 x_{4}\\ x_{2}^{\prime }&=22 x_{1}-8 x_{2}+3 x_{3}+19 x_{4}\\ x_{3}^{\prime }&=-10 x_{1}+3 x_{2}-9 x_{4}\\ x_{4}^{\prime }&=-27 x_{1}+9 x_{2}-3 x_{3}-23 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.464 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5}\\ x_{2}^{\prime }&=3 x_{2}\\ x_{3}^{\prime }&=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5}\\ x_{4}^{\prime }&=3 x_{1}+9 x_{3}+5 x_{4}-x_{5}\\ x_{5}^{\prime }&=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.235 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-4 x_{2}+x_{3}\\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}+x_{4}\\ x_{3}^{\prime }&=3 x_{3}-4 x_{4}\\ x_{4}^{\prime }&=4 x_{3}+3 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.264 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-8 x_{3}-3 x_{4}\\ x_{2}^{\prime }&=-18 x_{1}-x_{2}\\ x_{3}^{\prime }&=-9 x_{1}-3 x_{2}-25 x_{3}-9 x_{4}\\ x_{4}^{\prime }&=33 x_{1}+10 x_{2}+90 x_{3}+32 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.361 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\frac {x_{1}}{10}+\frac {3 x_{2}}{40}\\ x_{2}^{\prime }&=\frac {x_{1}}{10}-\frac {x_{2}}{5}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=4 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.177 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-4 x_{2}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-\frac {5 x_{2}}{2}\\ x_{2}^{\prime }&=\frac {9 x_{1}}{5}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}\\ x_{2}^{\prime }&=5 x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.051 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}\\ x_{2}^{\prime }&=-5 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3}\\ x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+2 x_{3}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ x_{3}^{\prime }&=-2 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
10.472 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.977 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+2 x_{2}\\ x_{2}^{\prime }&=-x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\frac {3 x_{1}}{4}-2 x_{2}\\ x_{2}^{\prime }&=x_{1}-\frac {5 x_{2}}{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\frac {4 x_{1}}{5}+2 x_{2}\\ x_{2}^{\prime }&=-x_{1}+\frac {6 x_{2}}{5}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.973 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2}\\ x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4}\\ x_{3}^{\prime }&=-\frac {x_{3}}{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2}\\ x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4}\\ x_{3}^{\prime }&=\frac {x_{3}}{10}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.194 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\frac {x_{1}}{2}-\frac {x_{2}}{8}\\ x_{2}^{\prime }&=2 x_{1}-\frac {x_{2}}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.647 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-4 x_{2}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=8 x_{1}-4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\frac {3 x_{1}}{2}+x_{2}\\ x_{2}^{\prime }&=-\frac {x_{1}}{4}-\frac {x_{2}}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2}\\ x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{3}^{\prime }&=-x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.287 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{3}\\ x_{3}^{\prime }&=x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.970 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-4 x_{2}\\ x_{2}^{\prime }&=4 x_{1}-7 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\frac {5 x_{1}}{2}+\frac {3 x_{2}}{2}\\ x_{2}^{\prime }&=-\frac {3 x_{1}}{2}+\frac {x_{2}}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+\frac {3 x_{2}}{2}\\ x_{2}^{\prime }&=-\frac {3 x_{1}}{2}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.367 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+9 x_{2}\\ x_{2}^{\prime }&=-x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=-4 x_{1}+x_{2}\\ x_{3}^{\prime }&=3 x_{1}+6 x_{2}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.114 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\frac {5 x_{1}}{2}+x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}-\frac {5 x_{2}}{2}+x_{3}\\ x_{3}^{\prime }&=x_{1}+x_{2}-\frac {5 x_{3}}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t}\\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}+t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t}\\ x_{2}^{\prime }&=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.544 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-5 x_{2}-\cos \left (t \right )\\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.664 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{-2 t}\\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-2 x_{2}+\frac {1}{t^{3}}\\ x_{2}^{\prime }&=8 x_{1}-4 x_{2}-\frac {1}{t^{2}}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.975 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-4 x_{1}+2 x_{2}+\frac {1}{t}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}+\frac {2}{t}+4\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.209 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{t}\\ x_{2}^{\prime }&=4 x_{1}+x_{2}-{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.184 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t}\\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}-{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.151 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\frac {5 x_{1}}{4}+\frac {3 x_{2}}{4}+2 t\\ x_{2}^{\prime }&=\frac {3 x_{1}}{4}-\frac {5 x_{2}}{4}+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.282 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+\sqrt {2}\, x_{2}+{\mathrm e}^{-t}\\ x_{2}^{\prime }&=\sqrt {2}\, x_{1}-2 x_{2}-{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.208 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.534 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\csc \left (t \right )\\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\sec \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.333 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\frac {x_{1}}{2}-\frac {x_{2}}{8}+\frac {{\mathrm e}^{-\frac {t}{2}}}{2}\\ x_{2}^{\prime }&=2 x_{1}-\frac {x_{2}}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.268 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t}\\ x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.284 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-x_{2}\\ x_{2}^{\prime }&=3 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{2}\\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.413 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-4 x_{2}\\ x_{2}^{\prime }&=4 x_{1}-7 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=4 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.966 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-x_{2}\\ x_{2}^{\prime }&=-\frac {5 x_{2}}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-4 x_{2}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}\\ x_{2}^{\prime }&=-5 x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}\\ x_{2}^{\prime }&=-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-\frac {5 x_{2}}{2}\\ x_{2}^{\prime }&=\frac {9 x_{1}}{5}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.828 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}-2\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.442 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+x_{2}-2\\ x_{2}^{\prime }&=x_{1}-2 x_{2}+1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-x_{2}-1\\ x_{2}^{\prime }&=2 x_{1}-x_{2}+5\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.560 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+2 y_{2}\\ y_{2}^{\prime }&=2 y_{1}+y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.479 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-\frac {5 y_{1}}{4}+\frac {3 y_{2}}{4}\\ y_{2}^{\prime }&=\frac {3 y_{1}}{4}-\frac {5 y_{2}}{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-\frac {4 y_{1}}{5}+\frac {3 y_{2}}{5}\\ y_{2}^{\prime }&=-\frac {2 y_{1}}{5}-\frac {11 y_{2}}{5}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.547 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}-4 y_{2}\\ y_{2}^{\prime }&=-y_{1}-y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-4 y_{2}\\ y_{2}^{\prime }&=-y_{1}-y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}-3 y_{2}\\ y_{2}^{\prime }&=2 y_{1}-y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.522 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-6 y_{1}-3 y_{2}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}-y_{2}-2 y_{3}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}-3 y_{3}\\ y_{3}^{\prime }&=-4 y_{1}+y_{2}-y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.136 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-8 y_{3}\\ y_{2}^{\prime }&=-4 y_{1}-4 y_{3}\\ y_{3}^{\prime }&=-8 y_{1}-4 y_{2}-6 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.878 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+5 y_{2}+8 y_{3}\\ y_{2}^{\prime }&=y_{1}-y_{2}-2 y_{3}\\ y_{3}^{\prime }&=-y_{1}-y_{2}-y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.990 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}-y_{2}+2 y_{3}\\ y_{2}^{\prime }&=12 y_{1}-4 y_{2}+10 y_{3}\\ y_{3}^{\prime }&=-6 y_{1}+y_{2}-7 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.034 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}-y_{2}-4 y_{3}\\ y_{2}^{\prime }&=4 y_{1}-3 y_{2}-2 y_{3}\\ y_{3}^{\prime }&=y_{1}-y_{2}-y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.052 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-2 y_{1}+2 y_{2}-6 y_{3}\\ y_{2}^{\prime }&=2 y_{1}+6 y_{2}+2 y_{3}\\ y_{3}^{\prime }&=-2 y_{1}-2 y_{2}+2 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.987 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+2 y_{2}-2 y_{3}\\ y_{2}^{\prime }&=-2 y_{1}+7 y_{2}-2 y_{3}\\ y_{3}^{\prime }&=-10 y_{1}+10 y_{2}-5 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.882 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+y_{2}-y_{3}\\ y_{2}^{\prime }&=3 y_{1}+5 y_{2}+y_{3}\\ y_{3}^{\prime }&=-6 y_{1}+2 y_{2}+4 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.807 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+4 y_{2}\\ y_{2}^{\prime }&=-y_{1}+7 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{2}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-7 y_{1}+4 y_{2}\\ y_{2}^{\prime }&=-y_{1}-11 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.418 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+y_{2}\\ y_{2}^{\prime }&=-y_{1}+y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}+12 y_{2}\\ y_{2}^{\prime }&=-3 y_{1}-8 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.379 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-10 y_{1}+9 y_{2}\\ y_{2}^{\prime }&=-4 y_{1}+2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-13 y_{1}+16 y_{2}\\ y_{2}^{\prime }&=-9 y_{1}+11 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{2}+y_{3}\\ y_{2}^{\prime }&=-4 y_{1}+6 y_{2}+y_{3}\\ y_{3}^{\prime }&=4 y_{2}+2 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.834 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {y_{1}}{3}+\frac {y_{2}}{3}-y_{3}\\ y_{2}^{\prime }&=-\frac {4 y_{1}}{3}-\frac {4 y_{2}}{3}+y_{3}\\ y_{3}^{\prime }&=-\frac {2 y_{1}}{3}+\frac {y_{2}}{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.841 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}+y_{2}-y_{3}\\ y_{2}^{\prime }&=-2 y_{1}+2 y_{3}\\ y_{3}^{\prime }&=-y_{1}+3 y_{2}-y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.818 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}-2 y_{2}-2 y_{3}\\ y_{2}^{\prime }&=-2 y_{1}+3 y_{2}-y_{3}\\ y_{3}^{\prime }&=2 y_{1}-y_{2}+3 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.975 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=6 y_{1}-5 y_{2}+3 y_{3}\\ y_{2}^{\prime }&=2 y_{1}-y_{2}+3 y_{3}\\ y_{3}^{\prime }&=2 y_{1}+y_{2}+y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.011 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-11 y_{1}+8 y_{2}\\ y_{2}^{\prime }&=-2 y_{1}-3 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=15 y_{1}-9 y_{2}\\ y_{2}^{\prime }&=16 y_{1}-9 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-3 y_{1}-4 y_{2}\\ y_{2}^{\prime }&=y_{1}-7 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-7 y_{1}+24 y_{2}\\ y_{2}^{\prime }&=-6 y_{1}+17 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.415 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-7 y_{1}+3 y_{2}\\ y_{2}^{\prime }&=-3 y_{1}-y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}+y_{2}\\ y_{2}^{\prime }&=y_{1}-y_{2}-2 y_{3}\\ y_{3}^{\prime }&=-y_{1}-y_{2}-y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.948 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-2 y_{1}+2 y_{2}+y_{3}\\ y_{2}^{\prime }&=-2 y_{1}+2 y_{2}+y_{3}\\ y_{3}^{\prime }&=-3 y_{1}+3 y_{2}+2 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-7 y_{1}-4 y_{2}+4 y_{3}\\ y_{2}^{\prime }&=y_{1}+y_{3}\\ y_{3}^{\prime }&=-9 y_{1}-5 y_{2}+6 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.666 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}-4 y_{2}-y_{3}\\ y_{2}^{\prime }&=3 y_{1}+6 y_{2}+y_{3}\\ y_{3}^{\prime }&=-3 y_{1}-2 y_{2}+3 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}-8 y_{2}-4 y_{3}\\ y_{2}^{\prime }&=-3 y_{1}-y_{2}-4 y_{3}\\ y_{3}^{\prime }&=y_{1}-y_{2}+9 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.015 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-5 y_{1}-y_{2}+11 y_{3}\\ y_{2}^{\prime }&=-7 y_{1}+y_{2}+13 y_{3}\\ y_{3}^{\prime }&=-4 y_{1}+8 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=5 y_{1}-y_{2}+y_{3}\\ y_{2}^{\prime }&=-y_{1}+9 y_{2}-3 y_{3}\\ y_{3}^{\prime }&=-2 y_{1}+2 y_{2}+4 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+10 y_{2}-12 y_{3}\\ y_{2}^{\prime }&=2 y_{1}+2 y_{2}+3 y_{3}\\ y_{3}^{\prime }&=2 y_{1}-y_{2}+6 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-4 y_{3}\\ y_{2}^{\prime }&=2 y_{1}-y_{2}+y_{3}\\ y_{3}^{\prime }&=2 y_{1}+3 y_{2}+y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.726 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{2}-2 y_{3}\\ y_{2}^{\prime }&=-y_{1}+5 y_{2}-3 y_{3}\\ y_{3}^{\prime }&=y_{1}+y_{2}+y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-2 y_{1}-12 y_{2}+10 y_{3}\\ y_{2}^{\prime }&=2 y_{1}-24 y_{2}+11 y_{3}\\ y_{3}^{\prime }&=2 y_{1}-24 y_{2}+8 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.906 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}-12 y_{2}+8 y_{3}\\ y_{2}^{\prime }&=y_{1}-9 y_{2}+4 y_{3}\\ y_{3}^{\prime }&=y_{1}-6 y_{2}+y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.797 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-4 y_{1}-y_{3}\\ y_{2}^{\prime }&=-y_{1}-3 y_{2}-y_{3}\\ y_{3}^{\prime }&=y_{1}-2 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.727 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-3 y_{1}-3 y_{2}+4 y_{3}\\ y_{2}^{\prime }&=4 y_{1}+5 y_{2}-8 y_{3}\\ y_{3}^{\prime }&=2 y_{1}+3 y_{2}-5 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-3 y_{1}-y_{2}\\ y_{2}^{\prime }&=y_{1}-y_{2}\\ y_{3}^{\prime }&=-y_{1}-y_{2}-2 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.692 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}+2 y_{2}\\ y_{2}^{\prime }&=-5 y_{1}+5 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.775 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-11 y_{1}+4 y_{2}\\ y_{2}^{\prime }&=-26 y_{1}+9 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+2 y_{2}\\ y_{2}^{\prime }&=-4 y_{1}+5 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=5 y_{1}-6 y_{2}\\ y_{2}^{\prime }&=3 y_{1}-y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-3 y_{1}-3 y_{2}+y_{3}\\ y_{2}^{\prime }&=2 y_{2}+2 y_{3}\\ y_{3}^{\prime }&=5 y_{1}+y_{2}+y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
18.567 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-3 y_{1}+3 y_{2}+y_{3}\\ y_{2}^{\prime }&=y_{1}-5 y_{2}-3 y_{3}\\ y_{3}^{\prime }&=-3 y_{1}+7 y_{2}+3 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.616 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}+y_{2}-y_{3}\\ y_{2}^{\prime }&=y_{2}+y_{3}\\ y_{3}^{\prime }&=y_{1}+y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.477 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-3 y_{1}+y_{2}-3 y_{3}\\ y_{2}^{\prime }&=4 y_{1}-y_{2}+2 y_{3}\\ y_{3}^{\prime }&=4 y_{1}-2 y_{2}+3 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.310 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=6 x-3 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y+t\\ y^{\prime }&=-4 x+3 y-1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=6 x-3 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y+{\mathrm e}^{t}\\ y^{\prime }&=x-y-{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.457 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=4 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-3 y\\ y^{\prime }&=-2 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=5 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=4 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+5 y+4 \,{\mathrm e}^{t} \cos \left (t \right )\\ y^{\prime }&=-2 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.558 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-4 y+{\mathrm e}^{t}\\ y^{\prime }&=x-y+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.947 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-5 y+\sin \left (t \right )\\ y^{\prime }&=x-2 y+\tan \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.345 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+\textit {f\_1} \left (t \right )\\ y^{\prime }&=-x+f_{2} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.316 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=6 x_{1}-3 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+x_{2}\\ x_{2}^{\prime }&=-4 x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3}\\ x_{2}^{\prime }&=2 x_{1}+2 x_{3}\\ x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.974 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=7 x_{1}-x_{2}+6 x_{3}\\ x_{2}^{\prime }&=-10 x_{1}+4 x_{2}-12 x_{3}\\ x_{3}^{\prime }&=-2 x_{1}+x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-7 x_{1}+6 x_{3}\\ x_{2}^{\prime }&=5 x_{2}\\ x_{3}^{\prime }&=6 x_{1}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}+3 x_{3}+6 x_{4}\\ x_{2}^{\prime }&=3 x_{1}+6 x_{2}+9 x_{3}+18 x_{4}\\ x_{3}^{\prime }&=5 x_{1}+10 x_{2}+15 x_{3}+30 x_{4}\\ x_{4}^{\prime }&=7 x_{1}+14 x_{2}+21 x_{3}+42 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.431 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}\\ x_{2}^{\prime }&=4 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.544 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-3 x_{2}\\ x_{2}^{\prime }&=-2 x_{1}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+x_{2}-x_{3}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}-x_{3}\\ x_{3}^{\prime }&=3 x_{1}+3 x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}\\ x_{2}^{\prime }&=x_{1}+2 x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{1}+10 x_{2}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-3 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=-x_{2}\\ x_{3}^{\prime }&=-x_{2}-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+x_{2}-2 x_{3}\\ x_{2}^{\prime }&=-x_{1}+2 x_{2}+x_{3}\\ x_{3}^{\prime }&=4 x_{1}+x_{2}-3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.083 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+2 x_{2}\\ x_{2}^{\prime }&=-x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}-3 x_{2}\\ x_{3}^{\prime }&=x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=3 x_{1}+x_{2}-2 x_{3}\\ x_{3}^{\prime }&=2 x_{1}+2 x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.245 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{3}\\ x_{2}^{\prime }&=x_{2}-x_{3}\\ x_{3}^{\prime }&=-2 x_{1}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.099 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}\\ x_{2}^{\prime }&=5 x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.713 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=4 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+2 x_{3}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ x_{3}^{\prime }&=-2 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{2}\\ x_{2}^{\prime }&=-2 x_{1}\\ x_{3}^{\prime }&=-3 x_{4}\\ x_{4}^{\prime }&=3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.285 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}\\ x_{2}^{\prime }&=x_{2}\\ x_{3}^{\prime }&=2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}+3 x_{3}\\ x_{2}^{\prime }&=2 x_{2}-x_{3}\\ x_{3}^{\prime }&=2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.659 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{2}+x_{3}\\ x_{2}^{\prime }&=2 x_{1}-3 x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{1}-x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.806 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{3}^{\prime }&=-3 x_{1}+2 x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-x_{2}\\ x_{2}^{\prime }&=-x_{2}\\ x_{3}^{\prime }&=-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{3}\\ x_{2}^{\prime }&=2 x_{2}+x_{3}\\ x_{3}^{\prime }&=2 x_{3}\\ x_{4}^{\prime }&=-x_{3}+2 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+x_{2}+2 x_{3}\\ x_{2}^{\prime }&=-x_{1}+x_{2}+x_{3}\\ x_{3}^{\prime }&=-2 x_{1}+x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.863 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-4 x_{1}-4 x_{2}\\ x_{2}^{\prime }&=10 x_{1}+9 x_{2}+x_{3}\\ x_{3}^{\prime }&=-4 x_{1}-3 x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.111 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}-3 x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{2}+2 x_{3}\\ x_{3}^{\prime }&=x_{1}-x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}\\ x_{3}^{\prime }&=3 x_{3}\\ x_{4}^{\prime }&=2 x_{3}+3 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3}\\ x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3}+{\mathrm e}^{t} \cos \left (2 t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.466 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+{\mathrm e}^{c t}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3}\\ x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.601 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right )\\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-4 x_{2}+{\mathrm e}^{t}\\ x_{2}^{\prime }&=x_{1}-x_{2}+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\sin \left (t \right )\\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\tan \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.674 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}+f_{1} \left (t \right )\\ x_{2}^{\prime }&=-x_{1}+f_{2} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.365 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{3}+{\mathrm e}^{2 t}\\ x_{2}^{\prime }&=2 x_{2}\\ x_{3}^{\prime }&=x_{2}+3 x_{3}+{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.134 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-x_{2}-2 x_{3}+{\mathrm e}^{t}\\ x_{2}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{3}^{\prime }&=2 x_{1}+x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.283 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}+{\mathrm e}^{3 t}\\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}+{\mathrm e}^{3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.484 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}-t^{2}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}+2 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+3 x_{2}+2 x_{3}+\sin \left (t \right )\\ x_{2}^{\prime }&=-x_{1}+2 x_{2}+x_{3}\\ x_{3}^{\prime }&=4 x_{1}-x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.103 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}-3 x_{3}+{\mathrm e}^{t}\\ x_{2}^{\prime }&=x_{1}+x_{2}+2 x_{3}\\ x_{3}^{\prime }&=x_{1}-x_{2}+4 x_{3}-{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-x_{2}+1\\ x_{2}^{\prime }&=-4 x_{2}-x_{3}+t\\ x_{3}^{\prime }&=5 x_{2}+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.897 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}-x_{3}+{\mathrm e}^{2 t}\\ x_{2}^{\prime }&=2 x_{1}+3 x_{2}-4 x_{3}+2 \,{\mathrm e}^{2 t}\\ x_{3}^{\prime }&=4 x_{1}+x_{2}-4 x_{3}+{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
25.460 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}+x_{3}-{\mathrm e}^{3 t}\\ x_{3}^{\prime }&=-3 x_{1}+x_{2}-x_{3}-{\mathrm e}^{3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
23.533 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3}+2 \,{\mathrm e}^{8 t}\\ x_{2}^{\prime }&=2 x_{1}+2 x_{3}+{\mathrm e}^{8 t}\\ x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3}+2 \,{\mathrm e}^{8 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.397 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-x^{2}-2 x y\\ y^{\prime }&=2 y-2 y^{2}-3 x y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-b x y+m\\ y^{\prime }&=b x y-g y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.036 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a x-b x y\\ y^{\prime }&=-c y+d x y\\ z^{\prime }&=z+x^{2}+y^{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-x \,y^{2}\\ y^{\prime }&=-y-y \,x^{2}\\ z^{\prime }&=1-z+x^{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \,y^{2}-x\\ y^{\prime }&=x \sin \left (\pi y\right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\cos \left (y\right )\\ y^{\prime }&=\sin \left (x\right )-1\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-1-y-{\mathrm e}^{x}\\ y^{\prime }&=x^{2}+y \left ({\mathrm e}^{x}-1\right )\\ z^{\prime }&=x+\sin \left (z\right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y^{2}\\ y^{\prime }&=x^{2}-y\\ z^{\prime }&={\mathrm e}^{z}-x\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y+z-2 \,{\mathrm e}^{-t}\\ y^{\prime }&=2 x+y-z-2 \,{\mathrm e}^{-t}\\ z^{\prime }&=-3 x+2 y+4 z+3 \,{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.220 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=-2 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x-4 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.979 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-5 x+3 y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-4 y\\ y^{\prime }&=4 x-7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.517 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-7 x+y-6 z\\ y^{\prime }&=10 x-4 y+12 z\\ z^{\prime }&=2 x-y+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+2 y+4 z\\ y^{\prime }&=2 x+2 z\\ z^{\prime }&=4 x+2 y+3 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.893 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y+z\\ y^{\prime }&=-x-3 y-z\\ z^{\prime }&=x+y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y+z\\ y^{\prime }&=-3 x+2 y+3 z\\ z^{\prime }&=x-y-2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.128 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=-2 x\\ z^{\prime }&=2 h\\ h^{\prime }&=-2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.253 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y+z\\ y^{\prime }&=-2 x+h\\ z^{\prime }&=2 h\\ h^{\prime }&=-2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.068 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=-\frac {\left (x_{1}^{2}+\sqrt {x_{1}^{2}+4 x_{2}^{2}}\right ) x_{1}}{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-x_{2}+1\\ x_{2}^{\prime }&=2 x_{1}-x_{2}+5\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.360 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-x^{3}-x y\\ y^{\prime }&=2 y-y^{5}-y \,x^{4}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x^{2}+y^{2}+1\\ y^{\prime }&=x^{2}-y^{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x^{2}+y^{2}-1\\ y^{\prime }&=2 x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.027 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=6 x-6 x^{2}-2 x y\\ y^{\prime }&=4 y-4 y^{2}-2 x y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\tan \left (x+y\right )\\ y^{\prime }&=x+x^{3}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.035 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&={\mathrm e}^{y}-x\\ y^{\prime }&={\mathrm e}^{x}+y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \textit {x\_}1^{\prime }&=-5 \textit {x\_}1+\textit {x\_}2\\ \textit {x\_}2^{\prime }&=\textit {x\_}1-5 \textit {x\_}2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{2}\\ x_{2}^{\prime }&=8 x_{1}-6 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-x_{2}\\ x_{2}^{\prime }&=-2 x_{1}+5 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-4 x_{1}-x_{2}\\ x_{2}^{\prime }&=x_{1}-6 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.567 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-4 x_{2}\\ x_{2}^{\prime }&=-8 x_{1}+4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.139 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-x_{2}\\ x_{2}^{\prime }&=5 x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{2}\\ x_{2}^{\prime }&=-2 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.733 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}\\ x_{2}^{\prime }&=5 x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}\\ x_{2}^{\prime }&=-5 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.606 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{2}\\ x_{2}^{\prime }&=-9 x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x&=\cos \left (t \right )\\ y+y^{\prime }&=4 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.601 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+5 x&=3 t^{2}\\ y+y^{\prime }&={\mathrm e}^{3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x&=3 t\\ x^{\prime }+2 y^{\prime }+y&=\cos \left (2 t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+y&=2 \sin \left (t \right )\\ x^{\prime }+y^{\prime }&=3 y-3 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.857 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+3 x-y&={\mathrm e}^{t}\\ 5 x-3 y^{\prime }&=y+2 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y^{\prime }-3 x^{\prime }-5 y&=5 t\\ 3 x^{\prime }-5 y^{\prime }-2 x&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.680 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x\\ y^{\prime }&=2 x+3 y\\ z^{\prime }&=3 y-2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}\\ x_{2}^{\prime }&=2 x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-3 x_{2}\\ x_{2}^{\prime }&=x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+2 x_{2}\\ x_{2}^{\prime }&=x_{2}-x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+4 x_{2}\\ x_{2}^{\prime }&=-4 x_{1}-6 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{2}\\ x_{2}^{\prime }&=-2 x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-3 x_{2}\\ x_{2}^{\prime }&=3 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}\\ x_{2}^{\prime }&=x_{2}-x_{3}\\ x_{3}^{\prime }&=x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}-x_{2}+3 x_{3}\\ x_{3}^{\prime }&=-x_{2}-3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.476 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{2}\\ x_{2}^{\prime }&=x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+5 x_{2}\\ x_{2}^{\prime }&=-x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}\\ x_{2}^{\prime }&=-x_{1}+4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.505 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}+5 \,{\mathrm e}^{4 t}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.930 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+x_{2}+t\\ x_{2}^{\prime }&=-2 x_{1}+x_{2}+1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{2 t}\\ x_{2}^{\prime }&=3 x_{1}-x_{2}+5 \,{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\tan \left (t \right ) x_{1}+3 \cos \left (t \right )^{2}\\ x_{2}^{\prime }&=x_{1}+\tan \left (t \right ) x_{2}+2 \sin \left (t \right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.024 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-4 x_{2}\\ x_{2}^{\prime }&=x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=-b x_{1}-a x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.303 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{2}\\ x_{2}^{\prime }&=-3 x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.656 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+3 x_{2}\\ x_{2}^{\prime }&=-2 x_{1}+5 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+x_{2}\\ x_{2}^{\prime }&=x_{2}-x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{2}+3 x_{3}\\ x_{2}^{\prime }&=3 x_{1}+x_{2}\\ x_{3}^{\prime }&=2 x_{1}-x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.142 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\frac {x_{1}}{t}\\ x_{2}^{\prime }&=x_{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\frac {x_{1}}{t}+t x_{2}\\ x_{2}^{\prime }&=-\frac {x_{1}}{t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}-7 x_{2}\\ x_{2}^{\prime }&=-x_{1}+4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-4 x_{2}\\ x_{2}^{\prime }&=4 x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-2 x_{2}\\ x_{2}^{\prime }&=5 x_{1}-5 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.878 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+2 x_{2}\\ x_{2}^{\prime }&=-2 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}\\ x_{2}^{\prime }&=5 x_{2}-7 x_{3}\\ x_{3}^{\prime }&=2 x_{2}-4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.986 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}\\ x_{2}^{\prime }&=x_{1}+5 x_{2}-x_{3}\\ x_{3}^{\prime }&=x_{1}+6 x_{2}-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=-x_{1}\\ x_{3}^{\prime }&=5 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+3 x_{3}\\ x_{2}^{\prime }&=-4 x_{2}\\ x_{3}^{\prime }&=-3 x_{1}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+6 x_{3}\\ x_{2}^{\prime }&=-2 x_{1}+x_{2}-2 x_{3}\\ x_{3}^{\prime }&=-x_{1}-2 x_{2}-4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.167 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{2}+x_{3}\\ x_{2}^{\prime }&=-2 x_{1}-x_{2}+x_{3}\\ x_{3}^{\prime }&=2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-x_{3}\\ x_{2}^{\prime }&=-3 x_{2}-x_{3}\\ x_{3}^{\prime }&=2 x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.407 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}-x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{3}^{\prime }&=-x_{1}+x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{2}+3 x_{3}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}+3 x_{3}\\ x_{3}^{\prime }&=2 x_{1}-x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}+3 x_{3}+4 x_{4}\\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}+2 x_{3}+x_{4}\\ x_{3}^{\prime }&=4 x_{1}+5 x_{2}+6 x_{3}+7 x_{4}\\ x_{4}^{\prime }&=7 x_{1}+6 x_{2}+5 x_{3}+4 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.758 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=-x_{1}\\ x_{3}^{\prime }&=-x_{4}\\ x_{4}^{\prime }&=x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.184 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+4 x_{2}\\ x_{2}^{\prime }&=2 x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-6 x_{2}\\ x_{2}^{\prime }&=3 x_{1}+5 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{2}+3 x_{3}\\ x_{2}^{\prime }&=3 x_{1}+x_{2}\\ x_{3}^{\prime }&=2 x_{1}-x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{2}\\ x_{2}^{\prime }&=-4 x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=-b x_{1}-a x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}\\ x_{2}^{\prime }&=-x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.518 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=x_{3}\\ x_{3}^{\prime }&=x_{1}+x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.967 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+2 x_{2}-x_{3}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{3}^{\prime }&=2 x_{1}+3 x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}\\ x_{2}^{\prime }&=x_{1}-3 x_{2}-x_{3}\\ x_{3}^{\prime }&=-x_{1}+x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=15 x_{1}-32 x_{2}+12 x_{3}\\ x_{2}^{\prime }&=8 x_{1}-17 x_{2}+6 x_{3}\\ x_{3}^{\prime }&=-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}\\ x_{2}^{\prime }&=x_{1}+4 x_{2}\\ x_{3}^{\prime }&=x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=3 x_{2}+2 x_{3}\\ x_{3}^{\prime }&=2 x_{1}-2 x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+x_{2}\\ x_{2}^{\prime }&=-x_{1}+5 x_{2}\\ x_{3}^{\prime }&=4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}-x_{1}\\ x_{2}^{\prime }&=-2 x_{1}-3 x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{1}+x_{2}-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{2}\\ x_{2}^{\prime }&=x_{1}\\ x_{3}^{\prime }&=x_{1}+2 x_{3}+x_{4}\\ x_{4}^{\prime }&=x_{2}+2 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.749 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+3 x_{2}\\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}\\ x_{3}^{\prime }&=x_{1}+x_{3}+x_{4}\\ x_{4}^{\prime }&=x_{2}+x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
1.436 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{2}\\ x_{2}^{\prime }&=x_{1}\\ x_{3}^{\prime }&=x_{1}-x_{4}\\ x_{4}^{\prime }&=x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}-x_{2}\\ x_{2}^{\prime }&=x_{1}-4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}-x_{2}+4 x_{3}\\ x_{2}^{\prime }&=-x_{2}\\ x_{3}^{\prime }&=-x_{1}-3 x_{2}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-3 x_{2}+{\mathrm e}^{2 t}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{2}\\ x_{2}^{\prime }&=-x_{1}+2 x_{2}+4 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+x_{2}+t \,{\mathrm e}^{3 t}\\ x_{2}^{\prime }&=3 x_{2}+{\mathrm e}^{3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+x_{2}+20 \,{\mathrm e}^{3 t}\\ x_{2}^{\prime }&=3 x_{1}+x_{2}+12 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.096 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+2 x_{2}+54 t \,{\mathrm e}^{3 t}\\ x_{2}^{\prime }&=-2 x_{1}+4 x_{2}+9 \,{\mathrm e}^{3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.071 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+4 x_{2}+8 \sin \left (2 t \right )\\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2}+8 \cos \left (2 t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.636 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+2 x_{2}-3 \,{\mathrm e}^{t}\\ x_{2}^{\prime }&=-2 x_{1}-x_{2}+6 \,{\mathrm e}^{t} t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-{\mathrm e}^{t}\\ x_{2}^{\prime }&=2 x_{1}-3 x_{2}+2 x_{3}+6 \,{\mathrm e}^{-t}\\ x_{3}^{\prime }&=x_{1}-2 x_{2}+2 x_{3}+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.398 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-2 x_{2}+2 x_{3}-{\mathrm e}^{3 t}\\ x_{2}^{\prime }&=2 x_{1}+4 x_{2}-x_{3}+4 \,{\mathrm e}^{3 t}\\ x_{3}^{\prime }&=3 x_{3}+3 \,{\mathrm e}^{3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.363 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-3 x_{2}+34 \sin \left (t \right )\\ x_{2}^{\prime }&=-4 x_{1}-2 x_{2}+17 \cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.331 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}\\ x_{2}^{\prime }&=2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}\\ x_{2}^{\prime }&=-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.502 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}\\ x_{2}^{\prime }&=3 x_{2}-x_{3}\\ x_{3}^{\prime }&=x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-x_{2}\\ x_{2}^{\prime }&=4 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}\\ x_{2}^{\prime }&=x_{2}-8 x_{3}\\ x_{3}^{\prime }&=2 x_{2}-7 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.877 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}+3 x_{3}\\ x_{2}^{\prime }&=2 x_{1}+3 x_{2}-2 x_{3}\\ x_{3}^{\prime }&=2 x_{2}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
22.493 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-8 x_{1}+6 x_{2}-3 x_{3}\\ x_{2}^{\prime }&=-12 x_{1}+10 x_{2}-3 x_{3}\\ x_{3}^{\prime }&=-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=6 x_{2}-7 x_{3}+3 x_{4}\\ x_{3}^{\prime }&=3 x_{3}-x_{4}\\ x_{4}^{\prime }&=-4 x_{2}+9 x_{3}-3 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.405 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{2}\\ x_{2}^{\prime }&=x_{1}\\ x_{3}^{\prime }&=x_{2}-x_{4}\\ x_{4}^{\prime }&=x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.207 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\left (2 t -1\right ) x_{1}\\ x_{2}^{\prime }&={\mathrm e}^{-t^{2}+t} x_{1}+x_{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=t \cot \left (t^{2}\right ) x_{1}+\frac {t \cos \left (t^{2}\right ) x_{3}}{2}\\ x_{2}^{\prime }&=\frac {x_{2}}{t}-x_{3}+2-t \sin \left (t \right )\\ x_{3}^{\prime }&=\csc \left (t^{2}\right ) x_{1}+x_{2}-x_{3}+1-t \cos \left (t \right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.024 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-6 x_{1}+x_{2}\\ x_{2}^{\prime }&=6 x_{1}-5 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=9 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=5 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=10 x_{1}-4 x_{2}\\ x_{2}^{\prime }&=4 x_{1}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-8 x_{1}+5 x_{2}\\ x_{2}^{\prime }&=-5 x_{1}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+4 x_{3}\\ x_{2}^{\prime }&=2 x_{2}\\ x_{3}^{\prime }&=-4 x_{1}-5 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.836 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}-x_{2}\\ x_{2}^{\prime }&=4 x_{1}-7 x_{2}\\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+13 x_{2}\\ x_{2}^{\prime }&=-x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}-10 x_{2}\\ x_{2}^{\prime }&=5 x_{1}+11 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.872 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-5 x_{2}+x_{3}\\ x_{2}^{\prime }&=4 x_{1}-9 x_{2}-x_{3}\\ x_{3}^{\prime }&=3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.381 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-4 x_{1}\\ x_{2}^{\prime }&=2 x_{1}+5 x_{2}-9 x_{3}\\ x_{3}^{\prime }&=5 x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.484 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-2 x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}-4 x_{2}+x_{3}\\ x_{3}^{\prime }&=2 x_{1}+2 x_{2}-3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.296 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3}\\ x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3}\\ x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.164 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-17 x_{1}-42 x_{3}\\ x_{2}^{\prime }&=-7 x_{1}+4 x_{2}-14 x_{3}\\ x_{3}^{\prime }&=7 x_{1}+18 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.983 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-16 x_{1}+30 x_{2}-18 x_{3}\\ x_{2}^{\prime }&=-8 x_{1}+8 x_{2}+16 x_{3}\\ x_{3}^{\prime }&=8 x_{1}-15 x_{2}+9 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.048 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-7 x_{1}-6 x_{2}-7 x_{3}\\ x_{2}^{\prime }&=-3 x_{1}-3 x_{2}-3 x_{3}\\ x_{3}^{\prime }&=7 x_{1}+6 x_{2}+7 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.976 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-x_{2}-2 x_{3}\\ x_{2}^{\prime }&=x_{1}+6 x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{1}+6 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-4 x_{2}-2 x_{3}\\ x_{2}^{\prime }&=-4 x_{1}-5 x_{2}-6 x_{3}\\ x_{3}^{\prime }&=4 x_{1}+8 x_{2}+7 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.495 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=7 x_{1}-2 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=4 x_{2}-x_{3}\\ x_{3}^{\prime }&=-x_{1}+x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}-x_{2}-2 x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{3}\\ x_{3}^{\prime }&=x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.983 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}-x_{3}\\ x_{2}^{\prime }&=-x_{2}\\ x_{3}^{\prime }&=x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+13 x_{2}\\ x_{2}^{\prime }&=-x_{1}-2 x_{2}\\ x_{3}^{\prime }&=2 x_{3}+4 x_{4}\\ x_{4}^{\prime }&=2 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.461 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=7 x_{1}-x_{4}\\ x_{2}^{\prime }&=6 x_{2}\\ x_{3}^{\prime }&=-x_{3}\\ x_{4}^{\prime }&=2 x_{1}+5 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.721 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-6 x_{1}+x_{2}+1\\ x_{2}^{\prime }&=6 x_{1}-5 x_{2}+{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=9 x_{1}-2 x_{2}+9 t\\ x_{2}^{\prime }&=5 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=10 x_{1}-4 x_{2}\\ x_{2}^{\prime }&=4 x_{1}+2 x_{2}+\frac {{\mathrm e}^{6 t}}{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3}+{\mathrm e}^{6 t}\\ x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3}+1\\ x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.658 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-2 x_{2}+x_{3}+t\\ x_{2}^{\prime }&=x_{1}-4 x_{2}+x_{3}\\ x_{3}^{\prime }&=2 x_{1}+2 x_{2}-3 x_{3}+1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.783 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+4 x_{2}\\ x_{2}^{\prime }&=8 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-6 x_{2}\\ x_{2}^{\prime }&=x_{1}-5 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}+9 x_{2}\\ x_{2}^{\prime }&=-2 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.847 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-4 x_{1}\\ x_{2}^{\prime }&=-4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=7 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=x_{1}+4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}-7 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}-x_{2}\\ x_{2}^{\prime }&=x_{1}-4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=10 x_{1}-8 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}\\ y_{2}^{\prime }&=3 y_{2}-2 y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+y_{2}\\ y_{2}^{\prime }&=3 y_{2}-y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}-y_{2}\\ y_{2}^{\prime }&=2 y_{1}+3 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{2}\\ y_{2}^{\prime }&=4 y_{2}-y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+y_{2}\\ y_{2}^{\prime }&=y_{1}-y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}\\ y_{2}^{\prime }&=y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}-y_{1}\\ y_{2}^{\prime }&=3 y_{1}-4 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y_{1}^{\prime }&=y_{1}+y_{2}\\ 2 y_{2}^{\prime }&=5 y_{2}-3 y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-2 y_{2}\\ y_{2}^{\prime }&=y_{1}+2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=1\\ y_{2}^{\prime }&=2 y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.413 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y_{1}^{\prime }+y_{2}^{\prime }-4 y_{1}-y_{2}&={\mathrm e}^{x}\\ y_{1}^{\prime }+3 y_{1}+y_{2}&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}\\ y_{2}^{\prime }&=-y_{1}+y_{3}\\ y_{3}^{\prime }&=-y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x-y&=0\\ x+y^{\prime }-2 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+x-5 y^{\prime }-4 y&=0\\ -y^{\prime }-2 x+y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+3 y&=0\\ 3 x-y^{\prime }+y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.370 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=0\\ x^{\prime }+x-y^{\prime }&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.021 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-3 x-4 y&=0\\ x+y^{\prime \prime }+y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.018 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }-y_{2}&=0\\ 4 y_{1}+y_{2}^{\prime }-4 y_{2}-2 y_{3}&=0\\ -2 y_{1}+y_{2}+y_{3}^{\prime }+y_{3}&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }-2 y_{1}+3 y_{2}-3 y_{3}&=0\\ -4 y_{1}+y_{2}^{\prime }+5 y_{2}-3 y_{3}&=0\\ -4 y_{1}+4 y_{2}+y_{3}^{\prime }-2 y_{3}&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x+2 y&=8\\ 2 x+y^{\prime }-2 y&=2 \,{\mathrm e}^{-t}-8\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-3 y+t \,{\mathrm e}^{-t}\\ y^{\prime }&=2 x-3 y+{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.970 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x-2 y&={\mathrm e}^{t}\\ -4 x+y^{\prime }-3 y&=1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.064 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-4 x+3 y&=\sin \left (t \right )\\ -2 x+y^{\prime }+y&=-2 \cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.199 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-y&=0\\ -x+y^{\prime }&={\mathrm e}^{t}+{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x+5 y&=0\\ -x+y^{\prime }-2 y&=\sin \left (2 t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.216 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 x+2 y^{\prime }&=-4 \,{\mathrm e}^{2 t}\\ 2 x^{\prime }-3 x+3 y^{\prime }-y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.068 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{\prime }+2 x+y^{\prime }-6 y&=5 \,{\mathrm e}^{t}\\ 4 x^{\prime }+2 x+y^{\prime }-8 y&=5 \,{\mathrm e}^{t}+2 t -3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-5 x+3 y&=2 \,{\mathrm e}^{3 t}\\ -x+y^{\prime }-y&=5 \,{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.209 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 x+y&=0\\ x+y^{\prime }-2 y&=-5 \,{\mathrm e}^{t} \sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+4 x+2 y&=\frac {2}{{\mathrm e}^{t}-1}\\ 6 x-y^{\prime }+3 y&=\frac {3}{{\mathrm e}^{t}-1}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+y&=\sec \left (t \right )\\ -2 x+y^{\prime }+y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}\\ x_{2}^{\prime }&=-4 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.413 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-3 x_{2}\\ x_{2}^{\prime }&=3 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}+3 x_{2}\\ x_{2}^{\prime }&=-3 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}+2 x_{2}-x_{3}\\ x_{3}^{\prime }&=x_{1}-x_{2}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{3}^{\prime }&=4 x_{1}-x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.136 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}-x_{3}\\ x_{3}^{\prime }&=-x_{1}+2 x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}-x_{3}\\ x_{2}^{\prime }&=3 x_{1}-4 x_{2}-3 x_{3}\\ x_{3}^{\prime }&=2 x_{1}-4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}\\ x_{3}^{\prime }&=-2 x_{2}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.988 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+x_{2}-2 x_{3}\\ x_{2}^{\prime }&=4 x_{1}+x_{2}\\ x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.018 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}+26 \sin \left (t \right )\\ x_{2}^{\prime }&=3 x_{1}+4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.304 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+8 x_{2}+9 t\\ x_{2}^{\prime }&=x_{1}+x_{2}+3 \,{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+2 x_{2}\\ x_{2}^{\prime }&=-3 x_{1}+4 x_{2}+\frac {{\mathrm e}^{3 t}}{1+{\mathrm e}^{2 t}}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.021 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-4 x_{1}-2 x_{2}+\frac {2}{{\mathrm e}^{t}-1}\\ x_{2}^{\prime }&=6 x_{1}+3 x_{2}-\frac {3}{{\mathrm e}^{t}-1}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{2 t}\\ x_{2}^{\prime }&=-2 x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.351 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}+x_{2}+\frac {4}{\sin \left (2 t \right )}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.585 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}+27 t\\ x_{2}^{\prime }&=-x_{1}+4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.881 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-x_{2}+{\mathrm e}^{t}\\ x_{2}^{\prime }&=4 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}+35 \,{\mathrm e}^{t} t^{{3}/{2}}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}+6 \,{\mathrm e}^{-t}\\ x_{3}^{\prime }&=2 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.830 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-2 x_{2}-x_{3}\\ x_{2}^{\prime }&=-x_{1}+x_{2}+x_{3}+12 t\\ x_{3}^{\prime }&=x_{1}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.502 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+4 x_{2}-2 x_{3}+{\mathrm e}^{t}\\ x_{2}^{\prime }&=x_{1}+x_{2}\\ x_{3}^{\prime }&=6 x_{1}-6 x_{2}+5 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
143.570 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}-x_{3}+4 \,{\mathrm e}^{t}\\ x_{2}^{\prime }&=x_{1}+x_{2}\\ x_{3}^{\prime }&=3 x_{1}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.126 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{2}+2 x_{3}\\ x_{2}^{\prime }&=x_{1}+2 x_{3}\\ x_{3}^{\prime }&=-2 x_{1}+x_{2}-x_{3}+4 \sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t}\\ x_{2}^{\prime }&=x_{1}+2 x_{2}-x_{3}\\ x_{3}^{\prime }&=x_{1}+x_{2}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.716 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{2}-x_{3}+2 \,{\mathrm e}^{2 t}\\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}-3 x_{3}\\ x_{3}^{\prime }&=-x_{1}+x_{2}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.289 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{3}+24 t\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ x_{3}^{\prime }&=3 x_{1}-x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.346 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-4 x-y\\ x^{\prime }&=2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-y^{\prime }+y&=-{\mathrm e}^{t}\\ x+y^{\prime }-y&={\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.992 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x+y^{\prime }+y&=t\\ 5 x+y^{\prime }+3 y&=t^{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.532 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x+2 y^{\prime }+7 y&={\mathrm e}^{t}+2\\ -2 x+y^{\prime }+3 y&={\mathrm e}^{t}-1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.009 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+y^{\prime }+3 y&={\mathrm e}^{-t}-1\\ x^{\prime }+2 x+y^{\prime }+3 y&=1+{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.387 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+y^{\prime }+2 y&=1+{\mathrm e}^{t}\\ y^{\prime }+2 y+z^{\prime }+z&={\mathrm e}^{t}+2\\ x^{\prime }-x+z^{\prime }+z&=3+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.603 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 y\\ y^{\prime }&=5 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=4 y+{\mathrm e}^{t}\\ y^{\prime \prime }&=4 x-{\mathrm e}^{t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\lambda _{1} x\\ y^{\prime }&=\lambda _{1} x-\lambda _{2} y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-18 x_{2}\\ x_{2}^{\prime }&=2 x_{1}-9 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.657 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+3 x_{2}\\ x_{2}^{\prime }&=5 x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+3 x_{2}\\ x_{2}^{\prime }&=-3 x_{1}+5 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-x_{2}\\ x_{2}^{\prime }&=5 x_{1}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+x_{2}\\ x_{2}^{\prime }&=x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t}\\ x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.292 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-x_{2}\\ x_{2}^{\prime }&=16 x_{1}-5 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-2 x_{2}\\ x_{2}^{\prime }&=3 x_{1}-4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-18 x_{2}\\ x_{2}^{\prime }&=2 x_{1}-9 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+3 x_{2}\\ x_{2}^{\prime }&=-3 x_{1}+5 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.153 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-18 x_{2}\\ x_{2}^{\prime }&=2 x_{1}-9 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-x_{2}\\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}-8\\ x_{2}^{\prime }&=x_{1}+x_{2}+3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.041 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}-8\\ x_{2}^{\prime }&=x_{1}+x_{2}+3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}\\ y_{2}^{\prime }&=y_{1}+y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}\\ y_{2}^{\prime }&=6 y_{1}+y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.256 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+y_{2}\\ y_{2}^{\prime }&=y_{1}+y_{2}+{\mathrm e}^{3 x}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.382 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+x y_{3}\\ y_{2}^{\prime }&=y_{2}+x^{3} y_{3}\\ y_{3}^{\prime }&=2 x y_{1}-y_{2}+{\mathrm e}^{x} y_{3}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.052 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 y\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 y\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=3 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.275 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y+t -1\\ y^{\prime }&=3 x+2 y-5 t -2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.896 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.696 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+4 y\\ y^{\prime }&=-2 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.204 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-2 y\\ y^{\prime }&=5 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.703 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+4 y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.119 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-3 y\\ y^{\prime }&=8 x-6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.392 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x\\ y^{\prime }&=3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x-y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x+6 y\\ y^{\prime }&=2 x+6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
10.458 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=4 x+5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.737 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y-5 t +2\\ y^{\prime }&=4 x-2 y-8 t -8\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-4 y\\ y^{\prime }&=4 x-7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.473 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=4 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+\sqrt {2}\, y\\ y^{\prime }&=\sqrt {2}\, x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.505 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+3 y\\ y^{\prime }&=-6 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+2 y\\ y^{\prime }&=-2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.358 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-5 y\\ y^{\prime }&=2 y-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.800 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=-4 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.611 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+2 y+z\\ y^{\prime }&=-2 x-y+3 z\\ z^{\prime }&=x+y+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.203 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y-z\\ y^{\prime }&=2 x-y-4 z\\ z^{\prime }&=3 x-y+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
44.693 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y-4 t +1\\ y^{\prime }&=-x+2 y+3 t +4\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
14.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y-t +3\\ y^{\prime }&=x+4 y+t -2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.852 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x+y-t +3\\ y^{\prime }&=-x-5 y+t +1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.395 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x y+1\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.051 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=t y+1\\ y^{\prime }&=-t x+y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.041 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-5 y\\ y^{\prime }&=4 x+8 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.211 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-7 y\\ y^{\prime }&=5 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.895 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+4 y-9 z\\ y^{\prime }&=6 x-y\\ z^{\prime }&=10 x+4 y+3 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
52.307 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=x+2 z\\ z^{\prime }&=z-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
35.100 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y+z+t -1\\ y^{\prime }&=2 x+y-z-3 t^{2}\\ z^{\prime }&=x+y+z+t^{2}-t +2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
25.626 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+4 y+{\mathrm e}^{-t} \sin \left (2 t \right )\\ y^{\prime }&=5 x+9 z+4 \,{\mathrm e}^{-t} \cos \left (2 t \right )\\ z^{\prime }&=y+6 z-{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✗ |
✓ |
✗ |
242.684 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+2 y+{\mathrm e}^{t}\\ y^{\prime }&=-x+3 y-{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
7.063 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x+5 y-9 z-8 \,{\mathrm e}^{-2 t}\\ y^{\prime }&=4 x+y+z+2 \,{\mathrm e}^{5 t}\\ z^{\prime }&=-2 y+3 z+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
105.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y+2 z+{\mathrm e}^{-t}-3 t\\ y^{\prime }&=3 x-4 y+z+2 \,{\mathrm e}^{-t}+t\\ z^{\prime }&=-2 x+5 y+6 z+2 \,{\mathrm e}^{-t}-t\\ \end {array} \]
|
✓ |
✗ |
✓ |
✗ |
343.143 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-7 y+4 \sin \left (t \right )+\left (t -4\right ) {\mathrm e}^{4 t}\\ y^{\prime }&=x+y+8 \sin \left (t \right )+\left (2 t +1\right ) {\mathrm e}^{4 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
20.901 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-4 y\\ y^{\prime }&=4 x-7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.256 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+5 y\\ y^{\prime }&=-2 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
12.253 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+\frac {y}{4}\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.292 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.861 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y+z\\ y^{\prime }&=6 x-y\\ z^{\prime }&=-x-2 y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.983 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+z\\ y^{\prime }&=x+y\\ z^{\prime }&=-2 x-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=4 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.207 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+2 y\\ y^{\prime }&=x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.142 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x+2 y\\ y^{\prime }&=-\frac {5 x}{2}+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.330 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\frac {5 x}{2}+2 y\\ y^{\prime }&=\frac {3 x}{4}-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.368 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=10 x-5 y\\ y^{\prime }&=8 x-12 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-6 x+2 y\\ y^{\prime }&=-3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.199 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y-z\\ y^{\prime }&=2 y\\ z^{\prime }&=y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.592 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-7 y\\ y^{\prime }&=5 x+10 y+4 z\\ z^{\prime }&=5 y+2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.145 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=x+2 y+z\\ z^{\prime }&=3 y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.054 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+z\\ y^{\prime }&=y\\ z^{\prime }&=x+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.337 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-y\\ y^{\prime }&=\frac {3 x}{4}-\frac {3 y}{2}+3 z\\ z^{\prime }&=\frac {x}{8}+\frac {y}{4}-\frac {z}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.708 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-y\\ y^{\prime }&=\frac {3 x}{4}-\frac {3 y}{2}+3 z\\ z^{\prime }&=\frac {x}{8}+\frac {y}{4}-\frac {z}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+4 y+2 z\\ y^{\prime }&=4 x-y-2 z\\ z^{\prime }&=6 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.796 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {x}{2}\\ y^{\prime }&=x-\frac {y}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.886 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y+4 z\\ y^{\prime }&=2 y\\ z^{\prime }&=x+y+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.819 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5}\\ y^{\prime }&=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5}\\ z^{\prime }&=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
151.866 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{3}-\frac {9 x_{4}}{5}\\ x_{2}^{\prime }&=\frac {51 x_{2}}{10}-x_{4}+3 x_{5}\\ x_{3}^{\prime }&=x_{1}+2 x_{2}-3 x_{3}\\ x_{4}^{\prime }&=x_{2}-\frac {31 x_{3}}{10}+4 x_{4}\\ x_{5}^{\prime }&=-\frac {14 x_{1}}{5}+\frac {3 x_{4}}{2}-x_{5}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
63.201 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y\\ y^{\prime }&=9 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.988 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-6 x+5 y\\ y^{\prime }&=-5 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+3 y\\ y^{\prime }&=-3 x+5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=12 x-9 y\\ y^{\prime }&=4 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
12.149 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y-z\\ y^{\prime }&=x+y-z\\ z^{\prime }&=x-y+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.369 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+2 y+4 z\\ y^{\prime }&=2 x+2 z\\ z^{\prime }&=4 x+2 y+3 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.790 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-4 y\\ y^{\prime }&=x+2 z\\ z^{\prime }&=2 y+5 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.799 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=3 y+z\\ z^{\prime }&=z-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.270 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=2 x+2 y-z\\ z^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.150 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+y\\ y^{\prime }&=4 y+z\\ z^{\prime }&=4 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+4 y\\ y^{\prime }&=-x+6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.989 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=z\\ y^{\prime }&=y\\ z^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.171 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=6 x-y\\ y^{\prime }&=5 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.576 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=-2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.253 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+y\\ y^{\prime }&=-2 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.549 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+5 y\\ y^{\prime }&=-2 x+6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.567 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-5 y\\ y^{\prime }&=5 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.332 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-8 y\\ y^{\prime }&=x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=z\\ y^{\prime }&=-z\\ z^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.614 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y+2 z\\ y^{\prime }&=3 x+6 z\\ z^{\prime }&=-4 x-3 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.989 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-12 y-14 z\\ y^{\prime }&=x+2 y-3 z\\ z^{\prime }&=x+y-2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+3 y-7\\ y^{\prime }&=-x-2 y+5\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.784 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+9 y+2\\ y^{\prime }&=-x+11 y+6\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+3 y\\ y^{\prime }&=-2 x+5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+4 y\\ y^{\prime }&=2 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=-x+2 y+4 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.353 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=6 x-7 y+10\\ y^{\prime }&=x-2 y-2 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.588 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=9 x+4 y\\ y^{\prime }&=-6 x-y\\ z^{\prime }&=6 x+4 y+3 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-3 y\\ y^{\prime }&=3 x+7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=2 x+5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x+y\\ y^{\prime }&=-4 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=y\\ z^{\prime }&=z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y-z\\ y^{\prime }&=-x+2 z\\ z^{\prime }&=-x-2 y+4 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y+2 t +1\\ y^{\prime }&=5 x+y+3 t -1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.308 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }-x&=y+t\\ x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.303 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+y^{\prime }-x&=y+t\\ x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }-x&=y+t +\sin \left (t \right )+\cos \left (t \right )\\ x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.304 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a x\\ y^{\prime }&=b\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a y\\ y^{\prime }&=-a x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a y\\ y^{\prime }&=b x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a x-y\\ y^{\prime }&=x+a y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a x+b y\\ y^{\prime }&=c x+b y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.360 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a x^{\prime }+b y^{\prime }&=\alpha x+\beta y\\ b x^{\prime }-a y^{\prime }&=\beta x-\alpha y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=2 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x+4 y&=0\\ y^{\prime }+2 x+5 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-5 x-2 y\\ y^{\prime }&=x-7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.689 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a_{1} x+b_{1} y+c_{1}\\ y^{\prime }&=a_{2} x+b_{2} y+c_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.179 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 y&=3 t\\ y^{\prime }-2 x&=4\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y-t^{2}+6 t +1&=0\\ -x+y^{\prime }&=-3 t^{2}+3 t +1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.052 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x-y&={\mathrm e}^{2 t}\\ y^{\prime }+x+5 y&={\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
7.132 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{2 t}+t\\ x^{\prime }-x+y^{\prime }+3 y&={\mathrm e}^{t}-1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.350 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }-y&={\mathrm e}^{t}\\ 2 x^{\prime }+y^{\prime }+2 y&=\cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{\prime }+9 y^{\prime }+2 x+31 y&={\mathrm e}^{t}\\ 3 x^{\prime }+7 y^{\prime }+x+24 y&=3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.534 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t}\\ 3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.991 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{\prime }+9 y^{\prime }+44 x+49 y&=t\\ 3 x^{\prime }+7 y^{\prime }+34 x+38 y&={\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x f \left (t \right )+y g \left (t \right )\\ y^{\prime }&=-x g \left (t \right )+y f \left (t \right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.024 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+\left (a x+b y\right ) f \left (t \right )&=g \left (t \right )\\ y^{\prime }+\left (c x+d y\right ) f \left (t \right )&=h \left (t \right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.026 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \cos \left (t \right )\\ y^{\prime }&=x \,{\mathrm e}^{-\sin \left (t \right )}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+y&=0\\ y^{\prime } t +x&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.018 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+2 x&=t\\ y^{\prime } t -\left (t +2\right ) x-t y&=-t\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.024 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+2 x-2 y&=t\\ y^{\prime } t +x+5 y&=t^{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} \left (1-\sin \left (t \right )\right ) x^{\prime }&=t \left (1-2 \sin \left (t \right )\right ) x+t^{2} y\\ t^{2} \left (1-\sin \left (t \right )\right ) y^{\prime }&=\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x+t \left (1-t \cos \left (t \right )\right ) y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }+y&=f \left (t \right )\\ x^{\prime \prime }+y^{\prime \prime }+y^{\prime }+x+y&=g \left (t \right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+y^{\prime }-3 x&=0\\ x^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{2 t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x-y^{\prime }&=2 t\\ x^{\prime \prime }+y^{\prime }-9 x+3 y&=\sin \left (2 t \right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.045 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+2 y&=0\\ x^{\prime \prime }-2 y^{\prime }&=2 t -\cos \left (2 t \right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.035 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }-y^{\prime } t -2 y&=0\\ t x^{\prime \prime }+2 x^{\prime }+t x&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+a y&=0\\ y^{\prime \prime }-a^{2} y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=a x+b y\\ y^{\prime \prime }&=c x+d y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=a_{1} x+b_{1} y+c_{1}\\ y^{\prime \prime }&=a_{2} x+b_{2} y+c_{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x+y&=-5\\ y^{\prime \prime }-4 x-3 y&=-3\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=\left (3 \cos \left (a t +b \right )^{2}-1\right ) c^{2} x+\frac {3 c^{2} y \sin \left (2 a t b \right )}{2}\\ y^{\prime \prime }&=\left (3 \sin \left (a t +b \right )^{2}-1\right ) c^{2} y+\frac {3 c^{2} x \sin \left (2 a t b \right )}{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+6 x+7 y&=0\\ y^{\prime \prime }+3 x+2 y&=2 t\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.036 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-a y^{\prime }+b x&=0\\ y^{\prime \prime }+a x^{\prime }+b y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a_{1} x^{\prime \prime }+b_{1} x^{\prime }+c_{1} x-A y^{\prime }&=B \,{\mathrm e}^{i \omega t}\\ a_{2} y^{\prime \prime }+b_{2} y^{\prime }+c_{2} y+A x^{\prime }&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+a \left (x^{\prime }-y^{\prime }\right )+b_{1} x&=c_{1} {\mathrm e}^{i \omega t}\\ y^{\prime \prime }+a \left (y^{\prime }-x^{\prime }\right )+b_{2} y&=c_{2} {\mathrm e}^{i \omega t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.048 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \operatorname {a11} x^{\prime \prime }+\operatorname {b11} x^{\prime }+\operatorname {c11} x+\operatorname {a12} y^{\prime \prime }+\operatorname {b12} y^{\prime }+\operatorname {c12} y&=0\\ \operatorname {a21} x^{\prime \prime }+\operatorname {b21} x^{\prime }+\operatorname {c21} x+\operatorname {a22} y^{\prime \prime }+\operatorname {b22} y^{\prime }+\operatorname {c22} y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.061 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-2 x^{\prime }-y^{\prime }+y&=0\\ y^{\prime \prime \prime }-y^{\prime \prime }+2 x^{\prime }-x&=t\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+y^{\prime \prime }+y^{\prime }&=\sinh \left (2 t \right )\\ 2 x^{\prime \prime }+y^{\prime \prime }&=2 t\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.062 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x^{\prime }+y^{\prime }&=0\\ x^{\prime \prime }+y^{\prime \prime }-x&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x\\ y^{\prime }&=3 x-2 y\\ z^{\prime }&=2 y+3 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.860 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x\\ y^{\prime }&=x-2 y\\ z^{\prime }&=x-4 y+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y-z\\ y^{\prime }&=x+y\\ z^{\prime }&=x+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-y+z&=0\\ -x+y^{\prime }-y&=t\\ z^{\prime }-x-z&=t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a x^{\prime }&=b c \left (y-z\right )\\ b y^{\prime }&=c a \left (z-x\right )\\ c z^{\prime }&=a b \left (x-y\right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.493 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=c y-b z\\ y^{\prime }&=a z-c x\\ z^{\prime }&=b x-a y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
8.559 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y-z\\ y^{\prime }&=y+z-x\\ z^{\prime }&=x-y+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.316 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+48 y-28 z\\ y^{\prime }&=-4 x+40 y-22 z\\ z^{\prime }&=-6 x+57 y-31 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=6 x-72 y+44 z\\ y^{\prime }&=4 x-4 y+26 z\\ z^{\prime }&=6 x-63 y+38 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
27.374 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a x+g y+\beta z\\ y^{\prime }&=g x+b y+\alpha z\\ z^{\prime }&=\beta x+\alpha y+c z\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
210.419 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }&=2 x-t\\ t^{3} y^{\prime }&=-x+t^{2} y+t\\ t^{4} z^{\prime }&=-x-t^{2} y+t^{3} z+t\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a t x^{\prime }&=b c \left (y-z\right )\\ b t y^{\prime }&=c a \left (z-x\right )\\ c t z^{\prime }&=a b \left (x-y\right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=a x_{2}+b x_{3} \cos \left (c t \right )+b x_{4} \sin \left (c t \right )\\ x_{2}^{\prime }&=-a x_{1}+b x_{3} \sin \left (c t \right )-b x_{4} \cos \left (c t \right )\\ x_{3}^{\prime }&=-b x_{1} \cos \left (c t \right )-b x_{2} \sin \left (c t \right )+a x_{4}\\ x_{4}^{\prime }&=-b x_{1} \sin \left (c t \right )+b x_{2} \cos \left (c t \right )-a x_{3}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.059 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x \left (x+y\right )\\ y^{\prime }&=y \left (x+y\right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\left (a y+b \right ) x\\ y^{\prime }&=\left (c x+d \right ) y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.035 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \left (a \left (p x+q y\right )+\alpha \right )\\ y^{\prime }&=y \left (\beta +b \left (p x+q y\right )\right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=h \left (a -x\right ) \left (c -x-y\right )\\ y^{\prime }&=k \left (b -y\right ) \left (c -x-y\right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y^{2}-\cos \left (x\right )\\ y^{\prime }&=-y \sin \left (x\right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.036 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x \,y^{2}+x+y\\ y^{\prime }&=y \,x^{2}-x-y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y-x \left (x^{2}+y^{2}\right )\\ y^{\prime }&=-x+y-y \left (x^{2}+y^{2}\right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.035 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y+x \left (x^{2}+y^{2}-1\right )\\ y^{\prime }&=x+y \left (x^{2}+y^{2}-1\right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) x^{\prime }&=-t x+y\\ \left (t^{2}+1\right ) y^{\prime }&=-x-t y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.025 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+y^{2}-t^{2}\right ) x^{\prime }&=-2 t x\\ \left (x^{2}+y^{2}-t^{2}\right ) y^{\prime }&=-2 t y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {x^{\prime }}^{2}+t x^{\prime }+a y^{\prime }-x&=0\\ x^{\prime } y^{\prime }+y^{\prime } t -y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.063 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x&=t x^{\prime }+f \left (x^{\prime }, y^{\prime }\right )\\ y&=y^{\prime } t +g \left (x^{\prime }, y^{\prime }\right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.067 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=a \,{\mathrm e}^{2 x}-{\mathrm e}^{-x}+{\mathrm e}^{-2 x} \cos \left (y\right )^{2}\\ y^{\prime \prime }&={\mathrm e}^{-2 x} \sin \left (y\right ) \cos \left (y\right )-\frac {\sin \left (y\right )}{\cos \left (y\right )^{3}}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.045 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=\frac {k x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}\\ y^{\prime \prime }&=\frac {k y}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y-z\\ y^{\prime }&=x^{2}+y\\ z^{\prime }&=x^{2}+z\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a x^{\prime }&=\left (b -c \right ) y z\\ b y^{\prime }&=\left (c -a \right ) z x\\ c z^{\prime }&=\left (a -b \right ) x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \left (y-z\right )\\ y^{\prime }&=y \left (z-x\right )\\ z^{\prime }&=z \left (x-y\right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }&=x y\\ y^{\prime }+z^{\prime }&=y z\\ x^{\prime }+z^{\prime }&=x z\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.056 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {x^{2}}{2}-\frac {y}{24}\\ y^{\prime }&=2 x y-3 z\\ z^{\prime }&=3 x z-\frac {y^{2}}{6}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.050 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \left (y^{2}-z^{2}\right )\\ y^{\prime }&=y \left (z^{2}-x^{2}\right )\\ z^{\prime }&=z \left (x^{2}-y^{2}\right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.089 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \left (y^{2}-z^{2}\right )\\ y^{\prime }&=-y \left (z^{2}+x^{2}\right )\\ z^{\prime }&=z \left (x^{2}+y^{2}\right )\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x \,y^{2}+x+y\\ y^{\prime }&=y \,x^{2}-x-y\\ z^{\prime }&=y^{2}-x^{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x-y\right ) \left (x-z\right ) x^{\prime }&=f \left (t \right )\\ \left (-x+y\right ) \left (y-z\right ) y^{\prime }&=f \left (t \right )\\ \left (z-x\right ) \left (z-y\right ) z^{\prime }&=f \left (t \right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.063 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{\prime }+3 x+2 y&={\mathrm e}^{t}\\ 4 x-3 y^{\prime }+3 y&=3 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.930 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 y\\ y^{\prime }&=2 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 y\\ y^{\prime }&=-4 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x\\ y^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 y\\ y^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.783 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-2 y\\ y^{\prime }&=2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x-3 y\\ y^{\prime }&=-x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 y\\ y^{\prime }&=-2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.776 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x-y\\ y^{\prime }&=-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=-2 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-6 y\\ y^{\prime }&=6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+3 y\\ y^{\prime }&=-x-14\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.250 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 y-3 x\\ y^{\prime }&=x+2 y-1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.745 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=3 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.661 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=3 y-3 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.273 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=3 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-y\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+y\\ y^{\prime }&=-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.747 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=3 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+4 y\\ y^{\prime }&=-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+2 y\\ y^{\prime }&=6 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-5 x+3 y\\ y^{\prime }&=2 x-10 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x\\ y^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.596 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=4 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.853 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-4 y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=9 y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=-2 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y+1\\ y^{\prime }&=x+y+2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-5 x+3 y+{\mathrm e}^{-t}\\ y^{\prime }&=2 x-10 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.996 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x+\cos \left (w t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.330 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+2 y+3\\ y^{\prime }&=7 x+5 y+2 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.356 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-3 y\\ y^{\prime }&=3 x+7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }-2 x-4 y&={\mathrm e}^{t}\\ x^{\prime }+y^{\prime }-y&={\mathrm e}^{4 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }-x&=-2 t\\ x^{\prime }+y^{\prime }-3 x-y&=t^{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.691 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }-x-3 y&={\mathrm e}^{t}\\ x^{\prime }+y^{\prime }+x&={\mathrm e}^{3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.292 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }-x-2 y&=2 \,{\mathrm e}^{t}\\ x^{\prime }+y^{\prime }-3 x-4 y&={\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.143 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+y^{\prime }-x-y&={\mathrm e}^{-t}\\ x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.264 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+y^{\prime }-3 x-y&=t\\ x^{\prime }+y^{\prime }-4 x-y&={\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }-x-6 y&={\mathrm e}^{3 t}\\ x^{\prime }+2 y^{\prime }-2 x-6 y&=t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.332 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }-x-3 y&=3 t\\ x^{\prime }+2 y^{\prime }-2 x-3 y&=1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.293 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }+2 y&=\sin \left (t \right )\\ x^{\prime }+y^{\prime }-x-y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
3.907 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-y^{\prime }-2 x+4 y&=t\\ x^{\prime }+y^{\prime }-x-y&=1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+y^{\prime }+x+5 y&=4 t\\ x^{\prime }+y^{\prime }+2 x+2 y&=2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }-x+5 y&=t^{2}\\ x^{\prime }+2 y^{\prime }-2 x+4 y&=2 t +1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.012 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+y^{\prime }+x+y&=t^{2}+4 t\\ x^{\prime }+y^{\prime }+2 x+2 y&=2 t^{2}-2 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.877 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{\prime }+2 y^{\prime }-x+y&=t -1\\ x^{\prime }+y^{\prime }-x&=t +2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+4 y^{\prime }+x-y&=3 \,{\mathrm e}^{t}\\ x^{\prime }+y^{\prime }+2 x+2 y&={\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.956 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+y^{\prime }-x-y&=-2 t\\ x^{\prime }+y^{\prime }+x-y&=t^{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.612 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+y^{\prime }-x-y&=1\\ x^{\prime }+y^{\prime }+2 x-y&=t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+4 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+3 y\\ y^{\prime }&=4 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+2 y+5 t\\ y^{\prime }&=3 x+4 y+17 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-2 y\\ y^{\prime }&=4 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-y\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+7 y\\ y^{\prime }&=3 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=7 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y-z\\ y^{\prime }&=2 x+3 y-4 z\\ z^{\prime }&=4 x+y-4 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y-z\\ y^{\prime }&=x+3 y+z\\ z^{\prime }&=-3 x-6 y+6 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.688 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 y\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+2 y\\ y^{\prime }&=x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+4 y\\ y^{\prime }&=3 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+5 y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-4 y\\ y^{\prime }&=2 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=4 x+5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=x+5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.261 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+7 y\\ y^{\prime }&=3 x+5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=3 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a x+b y\\ y^{\prime }&=c x+d y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.485 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-4 y-x \left (x^{2}+y^{2}\right )\\ y^{\prime }&=4 x+4 y-y \left (x^{2}+y^{2}\right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+\frac {x \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}}\\ y^{\prime }&=-x+\frac {y \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.105 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-x^{2}\\ y^{\prime }&=2 y-y^{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-y\\ y^{\prime }&=2 x+y+t^{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-4 y+\cos \left (2 t \right )\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+2 y\\ y^{\prime }&=6 x+3 y+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-4 y+{\mathrm e}^{3 t}\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+5 y\\ y^{\prime }&=-2 x+\cos \left (3 t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.882 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y+{\mathrm e}^{-t}\\ y^{\prime }&=4 x-2 y+{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=8 x+14 y\\ y^{\prime }&=7 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=8 x+14 y\\ y^{\prime }&=7 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x\\ y^{\prime }&=-5 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=11 x-2 y\\ y^{\prime }&=3 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+20 y\\ y^{\prime }&=40 x-19 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+2 y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.951 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+3 y\\ y^{\prime }&=-6 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.723 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-11 x-2 y\\ y^{\prime }&=13 x-9 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.840 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x-5 y\\ y^{\prime }&=10 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-4 y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-6 x+2 y\\ y^{\prime }&=-2 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x-y\\ y^{\prime }&=x-5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=13 x\\ y^{\prime }&=13 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x-4 y\\ y^{\prime }&=x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.389 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.565 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+5 x+y&={\mathrm e}^{t}\\ y^{\prime }-x-3 y&={\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.412 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=z\\ z^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.021 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=\frac {y^{2}}{x}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=3 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4}\\ y^{\prime }&=\frac {x}{2}-\frac {3 y}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+2 y&=0\\ y^{\prime }+y-x&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+5 x-2 y&=0\\ 2 x+y^{\prime }-y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.124 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-3 x+2 y&=0\\ y^{\prime }-x+3 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x-z&=0\\ x+y^{\prime }-y&=0\\ z^{\prime }+x+2 y-3 z&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.735 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\frac {x}{2}+2 y-3 z\\ y^{\prime }&=y-\frac {z}{2}\\ z^{\prime }&=-2 x+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.308 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }&=y\\ x^{\prime }-y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 y^{\prime }&=t\\ x^{\prime }-y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.172 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-y^{\prime }&=x+y-t\\ 2 x^{\prime }+3 y^{\prime }&=2 x+6\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }-y^{\prime }&=t\\ 3 x^{\prime }+2 y^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.960 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 x^{\prime }-3 y^{\prime }&=x+y\\ 3 x^{\prime }-y^{\prime }&=t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.133 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-4 y^{\prime }&=0\\ 2 x^{\prime }-3 y^{\prime }&=y+t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.406 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{\prime }+2 y^{\prime }&=\sin \left (t \right )\\ x^{\prime }-2 y^{\prime }&=x+y+t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.592 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x+9 y+12 \,{\mathrm e}^{-t}\\ y^{\prime }&=-5 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-7 x+6 y+6 \,{\mathrm e}^{-t}\\ y^{\prime }&=-12 x+5 y+37\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-7 x+10 y+18 \,{\mathrm e}^{t}\\ y^{\prime }&=-10 x+9 y+37\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.815 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-14 x+39 y+78 \sinh \left (t \right )\\ y^{\prime }&=-6 x+16 y+6 \cosh \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
9.080 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+4 y-2 z-2 \sinh \left (t \right )\\ y^{\prime }&=4 x+2 y-2 z+10 \cosh \left (t \right )\\ z^{\prime }&=-x+3 y+z+5\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+6 y-2 z+50 \,{\mathrm e}^{t}\\ y^{\prime }&=6 x+2 y-2 z+21 \,{\mathrm e}^{-t}\\ z^{\prime }&=-x+6 y+z+9\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.118 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x-2 y+4 z\\ y^{\prime }&=-2 x+y+2 z\\ z^{\prime }&=-4 x-2 y+6 z+{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.715 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y+3 z\\ y^{\prime }&=x-y+2 z+2 \,{\mathrm e}^{-t}\\ z^{\prime }&=-2 x+2 y-2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
7.682 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x+y-1-6 \,{\mathrm e}^{t}\\ y^{\prime }&=-4 x+3 y+4 \,{\mathrm e}^{t}-3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.190 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y+24 \sin \left (t \right )\\ y^{\prime }&=9 x-3 y+12 \cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.002 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x-4 y+10 \,{\mathrm e}^{t}\\ y^{\prime }&=3 x+14 y+6 \,{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.354 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-7 x+4 y+6 \,{\mathrm e}^{3 t}\\ y^{\prime }&=-5 x+2 y+6 \,{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x-3 y+z\\ y^{\prime }&=2 y+2 z+29 \,{\mathrm e}^{-t}\\ z^{\prime }&=5 x+y+z+39 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
86.302 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y-z+5 \sin \left (t \right )\\ y^{\prime }&=y+z-10 \cos \left (t \right )\\ z^{\prime }&=x+z+2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
10.524 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+3 y+z+5 \sin \left (2 t \right )\\ y^{\prime }&=x-5 y-3 z+5 \cos \left (2 t \right )\\ z^{\prime }&=-3 x+7 y+3 z+23 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
7.267 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+y-3 z+2 \,{\mathrm e}^{t}\\ y^{\prime }&=4 x-y+2 z+4 \,{\mathrm e}^{t}\\ z^{\prime }&=4 x-2 y+3 z+4 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
9.761 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+5 y+10 \sinh \left (t \right )\\ y^{\prime }&=19 x-13 y+24 \sinh \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.493 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=9 x-3 y-6 t\\ y^{\prime }&=-x+11 y+10 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.343 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=1+y\\ y^{\prime }&=1+x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{\prime }-y^{\prime }+3 x&=\sin \left (t \right )\\ x^{\prime }+y&=\cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
8.719 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-3 y\\ y^{\prime }&=5 x+6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.394 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x-10 y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.866 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=12 x+18 y\\ y^{\prime }&=-8 x-12 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=-x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-5 y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.960 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x+2 y\\ y^{\prime }&=3 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=2 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-2 y\\ y^{\prime }&=3 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
8.204 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=2 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=2 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=2 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=0\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.360 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-5 y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-3 y_{2}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}-2 y_{2}\\ y_{2}^{\prime }&=y_{1}+3 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.126 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+2 y_{2}+x -1\\ y_{2}^{\prime }&=3 y_{1}+2 y_{2}-5 x -2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {2 y_{1}}{x}-\frac {y_{2}}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}}\\ y_{2}^{\prime }&=2 y_{1}+1-6 x\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x\\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}-2 y_{2}\\ y_{2}^{\prime }&=y_{2}-y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right )\\ y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.047 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right )\\ y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.041 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2}\\ y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.041 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2}\\ y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.045 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-3 y_{2}+5 \,{\mathrm e}^{x}\\ y_{2}^{\prime }&=y_{1}+4 y_{2}-2 \,{\mathrm e}^{-x}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
16.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}-2 y_{1}+\sin \left (2 x \right )\\ y_{2}^{\prime }&=-3 y_{1}+y_{2}-2 \cos \left (3 x \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
22.823 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{2}\\ y_{2}^{\prime }&=3 y_{1}\\ y_{3}^{\prime }&=2 y_{3}-y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 x y_{1}-x^{2} y_{2}+4 x\\ y_{2}^{\prime }&={\mathrm e}^{x} y_{1}+3 \,{\mathrm e}^{-x} y_{2}-\cos \left (3 x \right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-3 y_{2}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-3 y_{2}+4 x -2\\ y_{2}^{\prime }&=y_{1}-2 y_{2}+3 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.334 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}\\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x\\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}+y_{2}-2 y_{3}\\ y_{2}^{\prime }&=3 y_{2}-2 y_{3}\\ y_{3}^{\prime }&=3 y_{1}+y_{2}-3 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.310 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=5 y_{1}-5 y_{2}-5 y_{3}\\ y_{2}^{\prime }&=-y_{1}+4 y_{2}+2 y_{3}\\ y_{3}^{\prime }&=3 y_{1}-5 y_{2}-3 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}+6 y_{2}+6 y_{3}\\ y_{2}^{\prime }&=y_{1}+3 y_{2}+2 y_{3}\\ y_{3}^{\prime }&=-y_{1}-4 y_{2}-3 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
8.445 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+2 y_{2}-3 y_{3}\\ y_{2}^{\prime }&=-3 y_{1}+4 y_{2}-2 y_{3}\\ y_{3}^{\prime }&=2 y_{1}+y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-2 y_{1}-y_{2}+y_{3}\\ y_{2}^{\prime }&=-y_{1}-2 y_{2}-y_{3}\\ y_{3}^{\prime }&=y_{1}-y_{2}-2 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+y_{2}+2 y_{3}\\ y_{2}^{\prime }&=y_{1}+y_{2}+2 y_{3}\\ y_{3}^{\prime }&=2 y_{1}+2 y_{2}+4 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.138 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}+y_{2}\\ y_{2}^{\prime }&=-y_{1}+2 y_{2}\\ y_{3}^{\prime }&=3 y_{3}-4 y_{4}\\ y_{4}^{\prime }&=4 y_{3}+3 y_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.182 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}\\ y_{2}^{\prime }&=-3 y_{1}+2 y_{3}\\ y_{3}^{\prime }&=y_{4}\\ y_{4}^{\prime }&=2 y_{1}-5 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
13.925 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+2 y_{2}\\ y_{2}^{\prime }&=3 y_{2}-2 y_{1}\\ y_{3}^{\prime }&=y_{3}\\ y_{4}^{\prime }&=2 y_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.916 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}+y_{4}\\ y_{2}^{\prime }&=y_{1}-y_{3}\\ y_{3}^{\prime }&=y_{4}\\ y_{4}^{\prime }&=y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.311 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+3 y\\ y^{\prime }&=2 y-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x\\ y^{\prime }&=-2 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-2 y\\ y^{\prime }&=2 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.798 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-2 y\\ y^{\prime }&=5 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x\\ y^{\prime }&=-2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
7.952 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-5 x-y+2\\ y^{\prime }&=3 x-y-3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.331 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y-6\\ y^{\prime }&=4 x-y+2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.694 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x\\ y^{\prime }&=2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.972 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.586 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 y\\ y^{\prime }&=3 \pi y-\frac {x}{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.990 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} p^{\prime }&=3 p-2 q-7 r\\ q^{\prime }&=-2 p+6 r\\ r^{\prime }&=\frac {73 q}{100}+2 r\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
186.193 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+2 \pi y\\ y^{\prime }&=4 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.077 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\beta y\\ y^{\prime }&=\gamma x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.223 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x-y\\ y^{\prime }&=2 x-5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x-3 y\\ y^{\prime }&=3 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+3 y\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=1\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.873 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x\\ y^{\prime }&=-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x-2 y\\ y^{\prime }&=-x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
11.620 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-5 x-2 y\\ y^{\prime }&=-x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=-x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\frac {x}{2}\\ y^{\prime }&=x-\frac {y}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+4 y\\ y^{\prime }&=9 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.064 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+4 y\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.167 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.384 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.265 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-2 y\\ y^{\prime }&=x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.055 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x-2 y\\ y^{\prime }&=-2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.203 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x-2 y\\ y^{\prime }&=-2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.163 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x-2 y\\ y^{\prime }&=-2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.139 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
11.382 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x+y\\ y^{\prime }&=2 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.212 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x+y\\ y^{\prime }&=2 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x+y\\ y^{\prime }&=2 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-2 y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-2 y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-2 y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=-2 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+2 y\\ y^{\prime }&=-4 x+6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x-5 y\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.063 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=-2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.711 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-6 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.996 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+4 y\\ y^{\prime }&=-3 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=-2 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+2 y\\ y^{\prime }&=-4 x+6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x-5 y\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=-2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.933 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-6 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+4 y\\ y^{\prime }&=-3 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.881 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\frac {9 x}{10}-2 y\\ y^{\prime }&=x+\frac {11 y}{10}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.452 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+10 y\\ y^{\prime }&=-x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x\\ y^{\prime }&=x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.502 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=-x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x-y\\ y^{\prime }&=x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.600 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x\\ y^{\prime }&=x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=-x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x-y\\ y^{\prime }&=x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+4 y\\ y^{\prime }&=3 x+6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+2 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 y\\ y^{\prime }&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x-y\\ y^{\prime }&=4 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {y}{10}\\ y^{\prime }&=\frac {z}{5}\\ z^{\prime }&=\frac {2 x}{5}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
7.155 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x\\ z^{\prime }&=2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+3 y\\ y^{\prime }&=3 x-2 y\\ z^{\prime }&=-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.521 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 z\\ y^{\prime }&=-y\\ z^{\prime }&=-3 x+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.232 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=2 y-z\\ z^{\prime }&=-y+2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.853 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=-2 y\\ z^{\prime }&=-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=-2 y\\ z^{\prime }&=z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x\\ y^{\prime }&=2 x-4 y\\ z^{\prime }&=-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x\\ y^{\prime }&=2 x-4 y\\ z^{\prime }&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.953 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=-2 y+z\\ z^{\prime }&=-2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=z\\ z^{\prime }&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.229 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=-2 y+3 z\\ z^{\prime }&=-x+3 y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x+3 y\\ y^{\prime }&=z-y\\ z^{\prime }&=5 x-5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-10 x+10 y\\ y^{\prime }&=28 x-y\\ z^{\prime }&=-\frac {8 z}{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.806 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=z-y\\ y^{\prime }&=z-x\\ z^{\prime }&=z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.873 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x\\ y^{\prime }&=-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.079 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=0\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\pi ^{2} x+\frac {187 y}{5}\\ y^{\prime }&=\sqrt {555}\, x+\frac {400617 y}{5000}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.883 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=-2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=-2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.055 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-4 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x-3 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
7.586 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=1-2 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-3 y\\ y^{\prime }&=6 x-7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.874 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+2 x&=15 y\\ y^{\prime } t&=x\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=5 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+4 y\\ y^{\prime }&=8 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+2 y\\ y^{\prime }&=3 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=5 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.953 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=2 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=-2 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 y\\ y^{\prime }&=8 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-13 y\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+2 y\\ y^{\prime }&=-2 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=8 x+2 y-17\\ y^{\prime }&=4 x+y-13\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.201 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=8 x+2 y+7 \,{\mathrm e}^{2 t}\\ y^{\prime }&=4 x+y-7 \,{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.243 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+3 y-6 \,{\mathrm e}^{3 t}\\ y^{\prime }&=x+6 y+2 \,{\mathrm e}^{3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.274 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=4 x+24 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.168 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-13 y\\ y^{\prime }&=x+19 \cos \left (4 t \right )-13 \sin \left (4 t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.005 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+3 y+5 \operatorname {Heaviside}\left (-2+t \right )\\ y^{\prime }&=x+6 y+17 \operatorname {Heaviside}\left (-2+t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
9.263 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+4 y\\ y^{\prime }&=8 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-5 y\\ y^{\prime }&=3 x-7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.358 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-5 y+4\\ y^{\prime }&=3 x-7 y+5\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.841 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+y\\ y^{\prime }&=6 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x y-6 y\\ y^{\prime }&=x-y-5\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x\\ y^{\prime }&=2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 y\\ y^{\prime }&=-x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.134 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 y\\ y^{\prime }&=-4 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-5 x+4 y\\ y^{\prime }&=2 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.515 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=6\\ y^{\prime }&=\cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=0\\ y^{\prime }&=-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x^{2}\\ y^{\prime }&={\mathrm e}^{t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.025 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}\\ x_{2}^{\prime }&=1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}+1\\ x_{2}^{\prime }&=x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+6 y\\ y^{\prime }&=4 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=8 x-y\\ y^{\prime }&=x+6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-2 y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+2 y\\ y^{\prime }&=2 y-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=1-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.870 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x+\sin \left (2 t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.748 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 t x_{1}^{2}\\ x_{2}^{\prime }&=\frac {x_{2}+t}{t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&={\mathrm e}^{t -x_{1}}\\ x_{2}^{\prime }&=2 \,{\mathrm e}^{x_{1}}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=\frac {y^{2}}{x}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\frac {x_{1}^{2}}{x_{2}}\\ x_{2}^{\prime }&=x_{2}-x_{1}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {{\mathrm e}^{-x}}{t}\\ y^{\prime }&=\frac {x \,{\mathrm e}^{-y}}{t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {y+t}{x+y}\\ y^{\prime }&=\frac {x-t}{x+y}\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.028 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {t -y}{-x+y}\\ y^{\prime }&=\frac {x-t}{-x+y}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {y+t}{x+y}\\ y^{\prime }&=\frac {t +x}{x+y}\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-9 y\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+t\\ y^{\prime }&=x-t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x+4 y&=0\\ y^{\prime }+2 x+5 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+5 y\\ y^{\prime }&=-x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{\prime }-y^{\prime }+3 x&=\sin \left (t \right )\\ x^{\prime }+y&=\cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=z-y\\ y^{\prime }&=z\\ z^{\prime }&=z-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.252 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+z\\ y^{\prime }&=x+z\\ z^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=y\\ y^{\prime \prime }&=x\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+y^{\prime }+x&=0\\ x^{\prime }+y^{\prime \prime }&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=3 x+y\\ y^{\prime }&=-2 x\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=x^{2}+y\\ y^{\prime }&=-2 x x^{\prime }+x\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x^{2}+y^{2}\\ y^{\prime }&=2 x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\frac {1}{y}\\ y^{\prime }&=\frac {1}{x}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.028 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {x}{y}\\ y^{\prime }&=\frac {y}{x}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.028 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {y}{x-y}\\ y^{\prime }&=\frac {x}{x-y}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\sin \left (x\right ) \cos \left (y\right )\\ y^{\prime }&=\cos \left (x\right ) \sin \left (y\right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{t} x^{\prime }&=\frac {1}{y}\\ {\mathrm e}^{t} y^{\prime }&=\frac {1}{x}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.035 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2}\\ y^{\prime }&=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=8 y-x\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.271 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=-2 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-5 y\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.830 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+z-x\\ y^{\prime }&=x-y+z\\ z^{\prime }&=x+y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.818 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y+z\\ y^{\prime }&=x+2 y-z\\ z^{\prime }&=x-y+2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.962 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y+z\\ y^{\prime }&=x+z\\ z^{\prime }&=y-2 z-3 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x-y&=-{\mathrm e}^{2 t}\\ y^{\prime }+3 x-2 y&=6 \,{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.051 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y-\cos \left (t \right )\\ y^{\prime }&=-y-2 x+\cos \left (t \right )+\sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.513 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+\tan \left (t \right )^{2}-1\\ y^{\prime }&=\tan \left (t \right )-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.450 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1}\\ y^{\prime }&=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x+\frac {1}{\cos \left (t \right )}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=1-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3-2 y\\ y^{\prime }&=2 x-2 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.963 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y+\sin \left (t \right )\\ y^{\prime }&=x+\cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y+{\mathrm e}^{t}\\ y^{\prime }&=x+y-{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-5 y+4 t -1\\ y^{\prime }&=x-2 y+t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.840 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y-x+{\mathrm e}^{t}\\ y^{\prime }&=x-y+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y&=t^{2}\\ -x+y^{\prime }&=t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.962 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }+y&={\mathrm e}^{-t}\\ 2 x^{\prime }+y^{\prime }+2 y&=\sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.828 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y-2 z+2-t\\ y^{\prime }&=1-x\\ z^{\prime }&=x+y-z+1-t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.997 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x+2 y&=2 \,{\mathrm e}^{-t}\\ y^{\prime }+y+z&=1\\ z^{\prime }+z&=1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.193 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+4 y\\ y^{\prime }&=x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=6 x+y\\ y^{\prime }&=4 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.565 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-4 y+1\\ y^{\prime }&=-x+5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.402 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+y+{\mathrm e}^{t}\\ y^{\prime }&=x+3 y-{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.861 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+4 y+\cos \left (t \right )\\ y^{\prime }&=-x-2 y+\sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=4+x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y+\sin \left (t \right )\\ y^{\prime }&=-x+y-\cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.796 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 t x+y\\ y^{\prime }&=3 x-y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.025 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y+4\\ y^{\prime }&=-2 x+y-3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y\\ y^{\prime }&=x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
7.013 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+t y\\ y^{\prime }&=t x-y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.021 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y+4\\ y^{\prime }&=-2 x+\sin \left (t \right ) y\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-4 y\\ y^{\prime }&=x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=3 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x\\ y^{\prime }&=-2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x+2 \sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.870 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-4 y+2 t\\ y^{\prime }&=x-3 y-3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y+1\\ y^{\prime }&=x+y-3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-4 y-4\\ y^{\prime }&=x-y-6\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4}+8\\ y^{\prime }&=\frac {x}{2}+y-\frac {23}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y-11\\ y^{\prime }&=-5 x+4 y-35\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.192 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y-3\\ y^{\prime }&=-x+y+1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-5 x+4 y-35\\ y^{\prime }&=-2 x+y-11\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=2 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=3 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=3 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=4 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-3 y\\ y^{\prime }&=8 x-6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4}\\ y^{\prime }&=\frac {3 x}{4}+\frac {5 y}{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.485 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\frac {3 x}{4}-\frac {7 y}{4}\\ y^{\prime }&=\frac {x}{4}+\frac {5 y}{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4}\\ y^{\prime }&=\frac {x}{2}+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.837 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-y\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=-5 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+6 y\\ y^{\prime }&=-x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=3 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.476 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=3 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-y\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=-5 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=4 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-4 y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-5 y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-\frac {5 y}{2}\\ y^{\prime }&=\frac {9 x}{5}-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=5 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.852 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=-5 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-4 y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-5 y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-5 y\\ y^{\prime }&=x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+2 y\\ y^{\prime }&=-x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {3 x}{4}-2 y\\ y^{\prime }&=x-\frac {5 y}{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\frac {4 x}{5}+2 y\\ y^{\prime }&=-x+\frac {6 y}{5}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a x+y\\ y^{\prime }&=-x+a y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-5 y\\ y^{\prime }&=x+a y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-5 y\\ y^{\prime }&=a x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4}\\ y^{\prime }&=a x+\frac {5 y}{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.161 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+a y\\ y^{\prime }&=-x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+a y\\ y^{\prime }&=-6 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.874 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a x+10 y\\ y^{\prime }&=-x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+a y\\ y^{\prime }&=8 x-6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.872 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} i^{\prime }&=\frac {i}{2}-\frac {v}{8}\\ v^{\prime }&=2 i-\frac {v}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-4 y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4}\\ y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\frac {3 x}{2}+y\\ y^{\prime }&=-\frac {x}{4}-\frac {y}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+\frac {5 y}{2}\\ y^{\prime }&=-\frac {5 x}{2}+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-\frac {y}{2}\\ y^{\prime }&=2 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+\frac {y}{2}\\ y^{\prime }&=-\frac {x}{2}+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-4 y\\ y^{\prime }&=4 x-7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\frac {5 x}{2}+\frac {3 y}{2}\\ y^{\prime }&=-\frac {3 x}{2}+\frac {y}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.849 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+\frac {3 y}{2}\\ y^{\prime }&=-\frac {3 x}{2}-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4}\\ y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+\frac {5 y}{2}\\ y^{\prime }&=-\frac {5 x}{2}+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+\frac {y}{2}\\ y^{\prime }&=-\frac {x}{2}+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=8 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=8 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=-8 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-4 y\\ y^{\prime }&=2 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.036 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y+x^{2}\\ y^{\prime }&=y-2 x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.027 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y \,x^{2}-3 x^{2}-4 y\\ y^{\prime }&=-2 x \,y^{2}+6 x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-x^{2}\\ y^{\prime }&=2 x y-3 y+2\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-x y\\ y^{\prime }&=y+2 x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.027 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2-y\\ y^{\prime }&=y-x^{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-x^{2}-x y\\ y^{\prime }&=\frac {y}{2}-\frac {y^{2}}{4}-\frac {3 x y}{4}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\left (x-y\right ) \left (1-x-y\right )\\ y^{\prime }&=x \left (2+y\right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.028 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y \left (2-x-y\right )\\ y^{\prime }&=-x-y-2 x y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\left (2+x\right ) \left (-x+y\right )\\ y^{\prime }&=y-x^{2}-y^{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.084 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+2 x y\\ y^{\prime }&=y-x^{2}-y^{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.026 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=x-\frac {x^{3}}{5}-\frac {y}{5}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.028 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \left (1-x-y\right )\\ y^{\prime }&=y \left (\frac {3}{4}-y-\frac {x}{2}\right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{3}^{\prime }&=-x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.090 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3}\\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3}\\ x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.148 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{3}\\ x_{3}^{\prime }&=x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3}\\ x_{2}^{\prime }&=2 x_{1}+2 x_{3}\\ x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-4 x_{1}+x_{2}\\ x_{2}^{\prime }&=x_{1}-5 x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{2}-4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+4 x_{2}+4 x_{3}\\ x_{2}^{\prime }&=3 x_{2}+2 x_{3}\\ x_{3}^{\prime }&=2 x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.577 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-4 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=-4 x_{1}+2 x_{2}-2 x_{3}\\ x_{3}^{\prime }&=2 x_{1}-2 x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+2 x_{2}-x_{3}\\ x_{2}^{\prime }&=-2 x_{1}+3 x_{2}-2 x_{3}\\ x_{3}^{\prime }&=-2 x_{1}+4 x_{2}-3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+6 x_{3}\\ x_{2}^{\prime }&=x_{1}+6 x_{2}+x_{3}\\ x_{3}^{\prime }&=6 x_{1}+x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.977 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3}\\ x_{2}^{\prime }&=2 x_{1}+2 x_{3}\\ x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.844 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.279 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3}\\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3}\\ x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.969 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+2 x_{3}\\ x_{2}^{\prime }&=2 x_{2}+2 x_{3}\\ x_{3}^{\prime }&=-x_{1}+x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.744 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{3}\\ x_{2}^{\prime }&=2 x_{1}\\ x_{3}^{\prime }&=-x_{1}+2 x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+3 x_{3}\\ x_{2}^{\prime }&=-2 x_{2}\\ x_{3}^{\prime }&=3 x_{1}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.208 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\frac {x_{1}}{2}-x_{2}-\frac {3 x_{3}}{2}\\ x_{2}^{\prime }&=\frac {3 x_{1}}{2}-2 x_{2}-\frac {3 x_{3}}{2}\\ x_{3}^{\prime }&=-2 x_{1}+2 x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+5 x_{2}+3 x_{3}-5 x_{4}\\ x_{2}^{\prime }&=2 x_{1}+3 x_{2}+2 x_{3}-4 x_{4}\\ x_{3}^{\prime }&=-x_{2}-2 x_{3}+x_{4}\\ x_{4}^{\prime }&=2 x_{1}+4 x_{2}+2 x_{3}-5 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-5 x_{1}+x_{2}-4 x_{3}-x_{4}\\ x_{2}^{\prime }&=-3 x_{2}\\ x_{3}^{\prime }&=x_{1}-x_{2}+x_{4}\\ x_{4}^{\prime }&=2 x_{1}-x_{2}+2 x_{3}-2 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+2 x_{2}-x_{4}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}+2 x_{4}\\ x_{3}^{\prime }&=3 x_{3}\\ x_{4}^{\prime }&=-x_{1}+2 x_{2}+2 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.821 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+8 x_{2}+5 x_{3}+3 x_{4}\\ x_{2}^{\prime }&=2 x_{1}+16 x_{2}+10 x_{3}+6 x_{4}\\ x_{3}^{\prime }&=5 x_{1}-14 x_{2}-11 x_{3}-3 x_{4}\\ x_{4}^{\prime }&=-x_{1}-8 x_{2}-5 x_{3}-3 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.186 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+2 x_{2}-2 x_{4}\\ x_{2}^{\prime }&=-x_{1}+3 x_{2}-x_{3}+x_{4}\\ x_{3}^{\prime }&=-2 x_{1}-2 x_{2}-4 x_{3}+2 x_{4}\\ x_{4}^{\prime }&=-7 x_{1}+x_{2}-7 x_{3}+3 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.787 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-5 x_{1}-2 x_{2}-x_{3}+2 x_{4}+3 x_{5}\\ x_{2}^{\prime }&=-3 x_{2}\\ x_{3}^{\prime }&=x_{1}-x_{3}-x_{5}\\ x_{4}^{\prime }&=2 x_{1}+x_{2}-4 x_{4}-2 x_{5}\\ x_{5}^{\prime }&=-3 x_{1}-2 x_{2}-x_{3}+2 x_{4}+x_{5}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.842 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{2}-2 x_{3}+3 x_{4}+2 x_{5}\\ x_{2}^{\prime }&=8 x_{1}+6 x_{2}+4 x_{3}-8 x_{4}-16 x_{5}\\ x_{3}^{\prime }&=-8 x_{1}-8 x_{2}-6 x_{3}+8 x_{4}-16 x_{5}\\ x_{4}^{\prime }&=8 x_{1}+7 x_{2}+4 x_{3}-9 x_{4}-16 x_{5}\\ x_{5}^{\prime }&=-3 x_{1}-5 x_{2}-3 x_{3}+5 x_{4}+7 x_{5}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
7.885 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+2 x_{2}+x_{3}\\ x_{2}^{\prime }&=-2 x_{1}+2 x_{2}+2 x_{3}\\ x_{3}^{\prime }&=2 x_{1}-3 x_{2}-3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.065 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-4 x_{2}-x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{2}+3 x_{3}\\ x_{3}^{\prime }&=3 x_{1}-4 x_{2}-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.750 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{2}-x_{3}\\ x_{2}^{\prime }&=x_{1}-x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{1}-2 x_{2}-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.998 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-4 x_{1}+2 x_{2}-x_{3}\\ x_{2}^{\prime }&=-6 x_{1}-3 x_{3}\\ x_{3}^{\prime }&=\frac {8 x_{2}}{3}-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.208 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-7 x_{1}+6 x_{2}-6 x_{3}\\ x_{2}^{\prime }&=-9 x_{1}+5 x_{2}-9 x_{3}\\ x_{3}^{\prime }&=-x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.013 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\frac {4 x_{1}}{3}+\frac {4 x_{2}}{3}-\frac {11 x_{3}}{3}\\ x_{2}^{\prime }&=-\frac {16 x_{1}}{3}-\frac {x_{2}}{3}+\frac {14 x_{3}}{3}\\ x_{3}^{\prime }&=3 x_{1}-2 x_{2}-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.790 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.364 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3}\\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3}\\ x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.179 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\frac {3 x_{1}}{4}+\frac {29 x_{2}}{4}-\frac {11 x_{3}}{2}\\ x_{2}^{\prime }&=-\frac {3 x_{1}}{4}+\frac {3 x_{2}}{4}-\frac {5 x_{3}}{2}\\ x_{3}^{\prime }&=\frac {5 x_{1}}{4}+\frac {11 x_{2}}{4}-\frac {5 x_{3}}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.779 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}-x_{2}+4 x_{3}+2 x_{4}\\ x_{2}^{\prime }&=-19 x_{1}-6 x_{2}+6 x_{3}+16 x_{4}\\ x_{3}^{\prime }&=-9 x_{1}-x_{2}+x_{3}+6 x_{4}\\ x_{4}^{\prime }&=-5 x_{1}-3 x_{2}+6 x_{3}+5 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.875 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+6 x_{2}+2 x_{3}-2 x_{4}\\ x_{2}^{\prime }&=2 x_{1}-3 x_{2}-6 x_{3}+2 x_{4}\\ x_{3}^{\prime }&=-4 x_{1}+8 x_{2}+3 x_{3}-4 x_{4}\\ x_{4}^{\prime }&=2 x_{1}-2 x_{2}-6 x_{3}+x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.611 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}-4 x_{2}+5 x_{3}+9 x_{4}\\ x_{2}^{\prime }&=-2 x_{1}-5 x_{2}+4 x_{3}+12 x_{4}\\ x_{3}^{\prime }&=-2 x_{1}-x_{3}+2 x_{4}\\ x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+3 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.277 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}-5 x_{2}+8 x_{3}+14 x_{4}\\ x_{2}^{\prime }&=-6 x_{1}-8 x_{2}+11 x_{3}+27 x_{4}\\ x_{3}^{\prime }&=-6 x_{1}-4 x_{2}+7 x_{3}+17 x_{4}\\ x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+4 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
7.717 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{2}-2 x_{4}\\ x_{2}^{\prime }&=-\frac {x_{1}}{2}+x_{2}-3 x_{3}-\frac {5 x_{4}}{2}\\ x_{3}^{\prime }&=3 x_{2}-5 x_{3}-3 x_{4}\\ x_{4}^{\prime }&=x_{1}+3 x_{2}-3 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.464 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+2 x_{2}\\ x_{2}^{\prime }&=\frac {x_{1}}{2}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-4 x_{2}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\frac {x_{1}}{2}-\frac {x_{2}}{4}\\ x_{2}^{\prime }&=x_{1}-\frac {x_{2}}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-\frac {5 x_{2}}{2}\\ x_{2}^{\prime }&=\frac {x_{1}}{2}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.873 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-4 x_{2}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-x_{2}\\ x_{2}^{\prime }&=3 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.665 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}\\ x_{2}^{\prime }&=5 x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{2}\\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=\frac {x_{1}}{2}+\frac {x_{2}}{2}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+4 x_{2}\\ x_{2}^{\prime }&=-x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.303 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2}\\ x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.331 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3}\\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3}\\ x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.233 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}-9 x_{2}\\ x_{2}^{\prime }&=x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{2}\\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-k_{1} x_{1}\\ x_{2}^{\prime }&=k_{1} x_{1}-k_{2} x_{2}\\ x_{3}^{\prime }&=k_{2} x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.376 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t}\\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}+t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.523 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t}\\ x_{2}^{\prime }&=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.656 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-5 x_{2}-\cos \left (t \right )\\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.792 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{-2 t}\\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.243 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=1-x_{2}+x_{3}\\ x_{2}^{\prime }&=2 x_{2}+t\\ x_{3}^{\prime }&=-2 x_{1}-x_{2}+3 x_{3}+{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.708 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {x_{3}}{2}+1\\ x_{2}^{\prime }&=-x_{1}-2 x_{2}+x_{3}+t\\ x_{3}^{\prime }&=\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {3 x_{3}}{2}+11 \,{\mathrm e}^{-3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.984 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-4 x_{1}+x_{2}+3 x_{3}+3 t\\ x_{2}^{\prime }&=-2 x_{2}\\ x_{3}^{\prime }&=-2 x_{1}+x_{2}+x_{3}+3 \cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.930 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-\frac {x_{1}}{2}+x_{2}+\frac {x_{3}}{2}\\ x_{2}^{\prime }&=x_{1}-x_{2}+x_{3}-\sin \left (t \right )\\ x_{3}^{\prime }&=\frac {x_{1}}{2}+x_{2}-\frac {x_{3}}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}+1\\ x_{2}^{\prime }&=x_{1}-2 x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
87.476 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-9 x_{2}\\ x_{2}^{\prime }&=x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-9 x_{2}\\ x_{2}^{\prime }&=x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{3}^{\prime }&=-3 x_{1}+2 x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-3 x_{2}-2 x_{3}\\ x_{2}^{\prime }&=8 x_{1}-5 x_{2}-4 x_{3}\\ x_{3}^{\prime }&=-4 x_{1}+3 x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.229 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-7 x_{1}+9 x_{2}-6 x_{3}\\ x_{2}^{\prime }&=-8 x_{1}+11 x_{2}-7 x_{3}\\ x_{3}^{\prime }&=-2 x_{1}+3 x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.526 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}+6 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2}-x_{3}\\ x_{3}^{\prime }&=-2 x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.152 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-8 x_{1}-16 x_{2}-16 x_{3}-17 x_{4}\\ x_{2}^{\prime }&=-2 x_{1}-10 x_{2}-8 x_{3}-7 x_{4}\\ x_{3}^{\prime }&=-2 x_{1}-2 x_{3}-3 x_{4}\\ x_{4}^{\prime }&=6 x_{1}+14 x_{2}+14 x_{3}+14 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
3.276 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}-2 x_{3}+3 x_{4}\\ x_{2}^{\prime }&=2 x_{1}-\frac {3 x_{2}}{2}-x_{3}+\frac {7 x_{4}}{2}\\ x_{3}^{\prime }&=-x_{1}+\frac {x_{2}}{2}-\frac {3 x_{4}}{2}\\ x_{4}^{\prime }&=-2 x_{1}+\frac {3 x_{2}}{2}+3 x_{3}-\frac {7 x_{4}}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.686 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-4 x_{2}\\ x_{2}^{\prime }&=4 x_{1}-7 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-4 x_{2}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}+3 x_{3}\\ x_{2}^{\prime }&=6 x_{1}+4 x_{2}+6 x_{3}\\ x_{3}^{\prime }&=-5 x_{1}-2 x_{2}-4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.168 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}\\ x_{2}^{\prime }&=-14 x_{1}-5 x_{2}+x_{3}\\ x_{3}^{\prime }&=15 x_{1}+5 x_{2}-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.160 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 y+x y\\ y^{\prime }&=x+4 x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=1+5 y\\ y^{\prime }&=1-6 x^{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=z\\ z^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.178 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=z+y\\ z^{\prime }&=y+z+x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.976 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y^{2}}{z}\\ z^{\prime }&=\frac {y}{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1-\frac {1}{z}\\ z^{\prime }&=\frac {1}{y-x}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.028 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-z\\ z^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {z^{2}}{y}\\ z^{\prime }&=\frac {y^{2}}{z}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y^{2}}{z}\\ z^{\prime }&=\frac {z^{2}}{y}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+z-x\\ y^{\prime }&=x-y+z\\ z^{\prime }&=x+y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x+y&=t^{2}\\ y^{\prime }+y+z&=2 t\\ z^{\prime }+z&=t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.224 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+5 x+y&=7 \,{\mathrm e}^{t}-27\\ -2 x+y^{\prime }+3 y&=-3 \,{\mathrm e}^{t}+12\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.131 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+z^{\prime }-2 z&={\mathrm e}^{2 x}\\ z^{\prime }+2 y^{\prime }-3 y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.048 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=x+{\mathrm e}^{t}+{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {2 z}{x^{2}}&=1\\ z^{\prime }+y&=x\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }-x-3 y&=t\\ y^{\prime } t -x+y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+6 x-y-3 z&=0\\ y^{\prime } t +23 x-6 y-9 z&=0\\ t z^{\prime }+x+y-2 z&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+5 x+y&={\mathrm e}^{t}\\ y^{\prime }-x+3 y&={\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.068 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 y\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=3 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y+t -1\\ y^{\prime }&=3 x+2 y-5 t -2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.354 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.300 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+4 y\\ y^{\prime }&=-2 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-2 y\\ y^{\prime }&=5 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+4 y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-3 y\\ y^{\prime }&=8 x-6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x\\ y^{\prime }&=3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x-y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x+6 y\\ y^{\prime }&=2 x+6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=4 x+5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y-5 t +2\\ y^{\prime }&=4 x-2 y-8 t -8\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x\\ y^{\prime }&=3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-2 y\\ y^{\prime }&=4 x-5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+4 y\\ y^{\prime }&=-2 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.499 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+2 y\\ y^{\prime }&=-17 x-5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.623 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x-y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-3 y\\ y^{\prime }&=8 x-6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-2 y\\ y^{\prime }&=5 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime }+7 y-3 z&=0\\ 7 y^{\prime }+63 y-36 z&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.127 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime }+2 y^{\prime }+3 y&=0\\ y^{\prime }+3 y-2 z&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+3 y+z&=0\\ z^{\prime }+3 y+5 z&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.172 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+3 y+2 z&=0\\ z^{\prime }+2 y-4 z&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 y-2 z&=0\\ z^{\prime }+y-2 z&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.712 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+z^{\prime }+6 y&=0\\ z^{\prime }+5 y+z&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime }+y^{\prime }+5 y-3 z&=x +{\mathrm e}^{x}\\ y^{\prime }+2 y-z&={\mathrm e}^{x}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.628 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime }+y+3 z&={\mathrm e}^{x}\\ y^{\prime }+3 y+4 z&={\mathrm e}^{2 x}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.676 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime }-3 y+2 z&={\mathrm e}^{x}\\ y^{\prime }+2 y-z&={\mathrm e}^{3 x}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.977 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime }+5 y-2 z&=x\\ y^{\prime }+4 y+z&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.500 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime }+7 y-9 z&={\mathrm e}^{x}\\ y^{\prime }-y-3 z&={\mathrm e}^{2 x}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-2 y-2 z&={\mathrm e}^{3 x}\\ z^{\prime }+5 y-2 z&={\mathrm e}^{4 x}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.312 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x+y^{\prime }+y&=0\\ 5 x+y^{\prime }+3 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-7 x+y&=0\\ y^{\prime }-2 x-5 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x-3 y&=t\\ y^{\prime }-3 x+2 y&={\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{\prime }+9 y^{\prime }+44 x+49 y&=t\\ 3 x^{\prime }+7 y^{\prime }+34 x+38 y&={\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.105 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-3 x-4 y&=0\\ x+y^{\prime \prime }+y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 y^{\prime }-2 x+2 y&=3 \,{\mathrm e}^{t}\\ 3 x^{\prime }+y^{\prime }+2 x+y&=4 \,{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.015 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{\prime }+9 y^{\prime }+2 x+31 y&={\mathrm e}^{t}\\ 3 x^{\prime }+7 y^{\prime }+x+24 y&=3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.639 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+4 x+3 y&=t\\ y^{\prime }+2 x+5 y&={\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.022 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=n y-m z\\ y^{\prime }&=L z-m x\\ z^{\prime }&=m x-L y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.360 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+y&=0\\ y^{\prime } t +x&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.021 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-7 x+y&=0\\ y^{\prime }-2 x-5 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+5 x+y&={\mathrm e}^{t}\\ y^{\prime }-x+3 y&={\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t}\\ 3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.148 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }&=t -2 x\\ y^{\prime } t&=t x+t y+2 x-t\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.024 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x-y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x\\ y^{\prime }&=-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.265 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=-5 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=-3 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.268 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+3 y\\ y^{\prime }&=-3 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y\\ y^{\prime }&=2 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=-5 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.254 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+3 y\\ y^{\prime }&=-3 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x-y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=-2 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=12 x-15 y\\ y^{\prime }&=4 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.051 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=5 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-13 y\\ y^{\prime }&=2 x-6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+2 y\\ y^{\prime }&=3 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+5 y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=8 x-5 y\\ y^{\prime }&=16 x+8 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=2 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+4 y+2 z\\ y^{\prime }&=4 x+5 y+2 z\\ z^{\prime }&=2 x+2 y+2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y+{\mathrm e}^{t}\\ y^{\prime }&=3 x-2 y+t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+3 y+1\\ y^{\prime }&=-6 x-4 y+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y+\cos \left (t \right )\\ y^{\prime }&=5 x-2 y+\sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \cos \left (t \right )-\sin \left (t \right ) y\\ y^{\prime }&=x \sin \left (t \right )+y \cos \left (t \right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\left (3 t -1\right ) x-\left (1-t \right ) y+t \,{\mathrm e}^{t^{2}}\\ y^{\prime }&=-\left (t +2\right ) x+\left (-2+t \right ) y-{\mathrm e}^{t^{2}}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.021 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-4 y\\ y^{\prime }&=2 y-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+6 y\\ y^{\prime }&=-2 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=8 x+y\\ y^{\prime }&=-4 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y+2 z\\ y^{\prime }&=-x+y+2 z\\ z^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y-z\\ y^{\prime }&=2 x-y+2 z\\ z^{\prime }&=2 x+2 y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.692 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w_{1}^{\prime }&=w_{2}\\ w_{2}^{\prime }&=\frac {a w_{1}}{z^{2}}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a y\\ y^{\prime }&=-a x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a x\\ y^{\prime }&=a y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a x+y\\ y^{\prime }&=a y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y\\ y^{\prime }&=x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=2 y-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 y\\ y^{\prime }&=-3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.280 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y\\ y^{\prime }&=-2 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+t\\ y^{\prime }&=-y+2 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+6 y\\ y^{\prime }&=x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+6 y+{\mathrm e}^{t}\\ y^{\prime }&=x+3 y-{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.929 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y+2 t\\ y^{\prime }&=3 y+t^{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y\\ y^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=4 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.518 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 y+2 t\\ y^{\prime }&=x-y+t^{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y+{\mathrm e}^{t}\\ y^{\prime }&=x-2 y-{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
9.130 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=x-y\\ z^{\prime }&=-2 x+2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=2 y+z\\ z^{\prime }&=x+3 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+z\\ y^{\prime }&=-y\\ z^{\prime }&=4 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=2 y+z\\ z^{\prime }&=x+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+z\\ y^{\prime }&=z-y\\ z^{\prime }&=y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x\\ y^{\prime }&=2 y+z\\ z^{\prime }&=-x-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\left (a -2\right ) x+y\\ y^{\prime }&=-x+\left (a -2\right ) y\\ z^{\prime }&=-a z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.377 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+t y&=-1\\ x^{\prime }+y^{\prime }&=2\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.026 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y&=3 t\\ y^{\prime }-t x^{\prime }&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.027 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-t y&=1\\ y^{\prime }-t x^{\prime }&=3\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.027 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime }-y&=1\\ y^{\prime }-2 x&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.024 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-y&=3\\ y^{\prime }-3 x^{\prime }&=-2 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+y^{\prime }&=1\\ y^{\prime }+x+{\mathrm e}^{x^{\prime }}&=1\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.045 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x x^{\prime }+y&=2 t\\ y^{\prime }+2 x^{2}&=1\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=1+x\\ y^{\prime }&=x+3 y-1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 y+a\\ y^{\prime }&=x-y+b\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
8.461 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a x+y\\ y^{\prime }&=-2 x+b y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=-2 c x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=-2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.696 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-6 y\\ y^{\prime }&=-2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-x y\\ y^{\prime }&=-y+x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-7 x y-a x\\ y^{\prime }&=-y+4 x y-a y\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-2 x y\\ y^{\prime }&=-y+x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-4 x y\\ y^{\prime }&=-2 y+x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \left (3-y\right )\\ y^{\prime }&=y \left (x-5\right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=7 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.909 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-y\\ y^{\prime }&=4 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
7.497 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=3 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
1.667 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 a x-y\\ y^{\prime }&=\left (a^{2}+9\right ) x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.858 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+4 y\\ y^{\prime }&=3 x-5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.589 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=-2 x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{2}-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=a x_{1}+5 x_{3}\\ x_{2}^{\prime }&=-x_{2}-2 x_{3}\\ x_{3}^{\prime }&=-3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.955 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}-2 x_{2}-x_{3}\\ x_{3}^{\prime }&=x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
21.972 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=a x_{1}\\ x_{2}^{\prime }&=a x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{2}+a x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}+x_{4}\\ x_{2}^{\prime }&=-x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{2}+x_{3}\\ x_{4}^{\prime }&=x_{1}-x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.952 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=x_{3}\\ x_{3}^{\prime }&=-a x_{3}-b x_{2}-c x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
40.116 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}\\ x_{2}^{\prime }&=-2 x_{2}\\ x_{3}^{\prime }&=x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.873 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y+y^{2}\\ y^{\prime }&=-2 y-x^{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.035 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x^{3}\\ y^{\prime }&=-y^{3}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }-3 x-2 y^{\prime }&=t\\ 2 x^{\prime }+3 x+2 y^{\prime }+8 y&=2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 y-5 z\\ z^{\prime }&=4 y-2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\sqrt {1-y^{2}}\\ x^{\prime }&=x+2 y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=8 x-y\\ y^{\prime }&=4 x+12 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-4 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-5 y\\ y^{\prime }&=2 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+2 y-z\\ y^{\prime }&=y+z\\ z^{\prime }&=z-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=9 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=4 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.462 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x-y+6 z\\ y^{\prime }&=-10 x+4 y-12 z\\ z^{\prime }&=-2 x+y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.896 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x+y^{\prime }&=\sin \left (t \right )+\cos \left (t \right )\\ x^{\prime }+y&=\cos \left (t \right )-\sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.970 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-2 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+2 y\\ y^{\prime }&=-5 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-y\\ y^{\prime }&=x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.376 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=6 x-3 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }-3 y^{\prime }&=2 \,{\mathrm e}^{2 t}\\ x^{\prime }-2 y^{\prime }&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y-3 z\\ z^{\prime }&=2 y-4 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-y\\ y^{\prime }&=-4 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.485 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x-y+6 z\\ y^{\prime }&=-10 x+4 y-12 z\\ z^{\prime }&=-2 x+y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+y-z\\ y^{\prime }&=x+3 y-z\\ z^{\prime }&=3 x+3 y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
7.832 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y-z\\ y^{\prime }&=y+3 z\\ z^{\prime }&=3 y+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+{\mathrm e}^{t}\\ y^{\prime }&=-2 x+3 y+1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.738 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y-5 t\\ y^{\prime }&=3 x+6 y-4\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y+3 \,{\mathrm e}^{2 t}\\ y^{\prime }&=-4 x+2 y+{\mathrm e}^{2 t} t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-7 y\\ y^{\prime }&=3 x-8 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+4 y\\ y^{\prime }&=-2 x+6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+4 y-y^{2}\\ y^{\prime }&=6 x-y+2 x y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\sin \left (x\right )-4 y\\ y^{\prime }&=\sin \left (2 x\right )-5 y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=8 x-y^{2}\\ y^{\prime }&=6 x^{2}-6 y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.051 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x^{2}-y\\ y^{\prime }&=x\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x^{3}-y\\ y^{\prime }&=x\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x y\\ y^{\prime }&=3 y^{2}-x^{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.036 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x^{2}\\ y^{\prime }&=2 y^{2}-x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y^{2}\\ y^{\prime }&=x^{2}-y\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.036 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x+y^{\prime }+y&=0\\ x^{\prime }-y^{\prime }-y&=t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
9.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 z&=5\\ y-z^{\prime }-x&=3-2 t\\ z+x^{\prime }&=-1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x+y&={\mathrm e}^{t}\\ x^{\prime }+x-y^{\prime }-y&=3 \,{\mathrm e}^{t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.045 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 x+y^{\prime }-2 y&=1\\ y^{\prime }+z^{\prime }+z&=2\\ 3 x+z^{\prime }+z&=3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x-y&=0\\ y^{\prime }+y-3 x&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x-2 y&=0\\ y^{\prime }-2 y-3 x&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y-x^{\prime \prime }+x&={\mathrm e}^{t}\\ y^{\prime }-x^{\prime }+x&={\mathrm e}^{-t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }-y&=0\\ y^{\prime }+2 y+z^{\prime }+2 z&=2\\ x+z^{\prime }-z&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.288 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=1\\ x^{\prime }+x+y^{\prime \prime }-9 y+z^{\prime }+z&=0\\ 5 x+z^{\prime \prime }-4 z&=2\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.057 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 z&=5\\ y-z^{\prime }-x&=3-2 t\\ z+x^{\prime }&=-1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.262 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y-x^{\prime }+x&=t\\ x^{\prime }+y^{\prime }+x-y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=8 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=8 x-2 y+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.121 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x+3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.983 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-9 x+6 y+t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-2 y-5 z+3\\ z^{\prime }&=y+2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.564 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=9 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.734 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=6 x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.840 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=6 x_{1}+4\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.216 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=6 x_{1}+4\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.062 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=6 x_{1}+4\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=6 x_{1}+9 \,{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.296 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=4 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=x_{3}\\ x_{3}^{\prime }&=6 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.965 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x\\ x^{\prime }&=-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.501 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime }&=2 v-1\\ v^{\prime }&=1+2 u\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=x\\ y^{\prime \prime }&=y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=x-2\\ y^{\prime \prime }&=2+y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+6 y&=x^{\prime }\\ 3 x-x^{\prime }&=2 y^{\prime }\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x+2 y&=1\\ 2 x+y^{\prime }-2 y&=t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.818 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }+2 x-y&=-\sin \left (t \right )\\ x^{\prime }-3 x+y^{\prime }+2 y&=4 \cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.350 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 y^{\prime }+8 x&=32 t\\ y^{\prime \prime }+3 x^{\prime }-2 y&=60 \,{\mathrm e}^{-t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 y^{\prime }&={\mathrm e}^{t}\\ x^{\prime }+y^{\prime }&=\sqrt {t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 y^{\prime }&=x y\\ 3 x^{\prime }-y^{\prime }&=\sin \left (t \right )\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} r^{\prime \prime }\left (t \right )&=r \left (t \right )+y\\ y^{\prime \prime }&=5 r \left (t \right )-3 y+t^{2}\\ \end {array} \]
|
✗ |
✗ |
✓ |
✓ |
0.027 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y x^{\prime }&=t^{2}\\ 2 x^{\prime \prime }-y^{\prime }&=5 t\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+y^{\prime }+x&=y+\sin \left (t \right )\\ y^{\prime \prime }+x^{\prime }-y&=2 t^{2}-x\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.042 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=x-y\\ z^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y z\\ y^{\prime }&=x z\\ z^{\prime }&=x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.034 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x y\\ y^{\prime }&=1+y^{2}\\ z^{\prime }&=z\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+t z^{\prime }+z&=t\\ y^{\prime } t +z&=\ln \left (t \right )\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=z\\ z^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.391 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+z\\ y^{\prime }&=x+z\\ z^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+6 x+3 y^{\prime }+2 y&=0\\ x^{\prime }+5 x+2 y^{\prime }+3 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+2 y^{\prime }+7 y&=0\\ 2 x^{\prime }+y^{\prime }+x+5 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+5 x+3 y^{\prime }-11 y&=0\\ x^{\prime }+3 x+y^{\prime }-7 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.361 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 x+4 y&=0\\ 3 x+2 y^{\prime }+y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x+2 y&=0\\ 3 x+y^{\prime }+y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.748 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+4 x+3 y^{\prime }+4 y&=0\\ x^{\prime }+2 x+2 y^{\prime }+2 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x+2 y^{\prime }+3 y&=0\\ x^{\prime }-2 x+5 y^{\prime }&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x-y&=0\\ 5 x+y^{\prime }-3 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x-y^{\prime }-5 y&=0\\ x^{\prime }+x+2 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }-6 x+3 y^{\prime }-2 y&=0\\ 7 x^{\prime }+4 x+7 y^{\prime }+20 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x+2 y&=8\\ 2 x+y^{\prime }-2 y&=2 \,{\mathrm e}^{-t}-8\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.956 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 y&=4 \,{\mathrm e}^{2 t}\\ x+y^{\prime }-y&=2 \,{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+2 y^{\prime }+7 y&=3 t -15\\ 2 x^{\prime }+y^{\prime }+x+5 y&=9 t -7\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x-y^{\prime }-y&=0\\ 2 x^{\prime }-9 x+y^{\prime }+4 y&=15 \,{\mathrm e}^{-3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x-y^{\prime }-2 y&=8 t\\ x^{\prime }-2 x+y&=16 \,{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }-x-y^{\prime }+y&=4 t \,{\mathrm e}^{-t}-3 \,{\mathrm e}^{-t}\\ x^{\prime }+4 x-2 y^{\prime }-4 y&=2 t \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.896 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }-x+7 y^{\prime }+3 y&=90 \sin \left (2 t \right )\\ x^{\prime }-5 x+8 y^{\prime }-3 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.455 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t}\\ y^{\prime \prime }&=x-{\mathrm e}^{-2 t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-5 x+y^{\prime }+2 z&=24 \,{\mathrm e}^{-t}\\ x^{\prime }-x-y&=0\\ 5 y^{\prime }-11 y+2 z^{\prime }-2 z&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.583 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x-2 y&={\mathrm e}^{-t}\\ y^{\prime }-x+4 y&=\sin \left (2 t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+2 y-z&=t^{2}\\ y^{\prime }+3 x-y+4 z&={\mathrm e}^{t}\\ z^{\prime }-2 x+y-z&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
69.499 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z+x^{\prime }&=x\\ y^{\prime }-2 x&=y+3 t\\ z^{\prime }+4 y&=z-\cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.360 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+5 x-4 y&=0\\ y^{\prime }-x+2 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x-5 y&=0\\ y^{\prime }+4 x+5 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 x+3 y&=0\\ -2 x+y^{\prime }+3 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x-6 y&=0\\ y^{\prime }&=x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+8 y\\ y^{\prime }&=-2 x-7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-12 x-7 y\\ y^{\prime }&=19 x+11 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.238 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-y&=t\\ x+y^{\prime }&=t^{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x+4 y&=8 \,{\mathrm e}^{t}\\ -x+y^{\prime }-y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 x+y&={\mathrm e}^{-t}\\ y^{\prime }-3 x+2 y&=t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x-y&=100 \sin \left (t \right )\\ y^{\prime }-4 x-y&=36 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-3 x-6 y&=9-9 t\\ y^{\prime }+3 x+3 y&=9 t \,{\mathrm e}^{-3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.245 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-3 y+t \,{\mathrm e}^{-t}\\ y^{\prime }&=2 x-3 y+{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+4 x+2 y-z&=12 \,{\mathrm e}^{t}\\ y^{\prime }-2 x-5 y+3 z&=0\\ z^{\prime }+4 x+z&=30 \,{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.823 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+y^{\prime }+6 x&=0\\ y^{\prime \prime }-x^{\prime }+6 y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.059 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}\\ x_{2}^{\prime }&=-3 x_{1}+6 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.974 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+4 x_{2}\\ x_{2}^{\prime }&=-2 x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.930 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 \sin \left (t \right ) x_{1}+\ln \left (t \right ) x_{2}\\ x_{2}^{\prime }&=\frac {x_{1}}{-2+t}+\frac {{\mathrm e}^{t} x_{2}}{1+t}\\ \end {array} \]
|
✗ |
✓ |
✗ |
✓ |
0.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-6 y+1\\ y^{\prime }&=6 x-7 y+1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.061 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-6 y\\ y^{\prime }&=6 x-7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=2 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.977 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.985 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.951 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=-x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.906 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y-z\\ y^{\prime }&=z-x\\ z^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.774 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+\left (1-t \right ) x_{2}\\ x_{2}^{\prime }&=\frac {x_{1}}{t}-x_{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}-x_{3}+x_{4}\\ x_{2}^{\prime }&=-x_{2}+x_{4}\\ x_{3}^{\prime }&=x_{3}-x_{4}\\ x_{4}^{\prime }&=2 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.994 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}+2 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=2 x_{1}+2 x_{2}-4 x_{3}\\ x_{3}^{\prime }&=2 x_{1}-4 x_{2}+2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
1.528 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-10 x_{1}+x_{2}+7 x_{3}\\ x_{2}^{\prime }&=-9 x_{1}+4 x_{2}+5 x_{3}\\ x_{3}^{\prime }&=-17 x_{1}+x_{2}+12 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.788 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.873 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-x_{2}+3 \,{\mathrm e}^{2 t}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}+2 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.504 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1\\ x_{2}^{\prime }&=x_{1}+t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.291 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-6 y+1\\ y^{\prime }&=6 x-7 y+1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.002 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }&=3 x-2 y\\ y^{\prime } t&=x+y-t^{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y+2 t^{2}\\ y^{\prime }&=5 x+y-1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.577 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}\\ x_{2}^{\prime }&=4 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.129 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} N_{1}^{\prime }&=4 N_{1}-6 N_{2}\\ N_{2}^{\prime }&=8 N_{1}-10 N_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
8.791 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-x_{2}+3 \,{\mathrm e}^{2 t}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}+2 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1\\ x_{2}^{\prime }&=x_{1}+t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.172 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-6 y+1\\ y^{\prime }&=6 x-7 y+1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.967 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }&=3 x-2 y\\ y^{\prime } t&=x+y-t^{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.041 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y+2 t^{2}\\ y^{\prime }&=5 x+y-1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.746 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=4 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.840 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=2 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=-x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=-x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.872 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=2 y-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.689 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=9 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.001 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=-3 x+6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.908 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=z\\ z^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
6.596 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c_{1}^{\prime }&=-\frac {k c_{1}}{V_{1}}+\frac {k c_{2}}{V_{1}}\\ c_{2}^{\prime }&=\frac {k c_{1}}{V_{2}}-\frac {k c_{2}}{V_{2}}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.439 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a \left (b -x\right )-c f y\\ y^{\prime }&=d \left (x-y\right )-c f y-a y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.362 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+2 y\\ y^{\prime }&=-3 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-2 y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x+y\\ y^{\prime }&=-x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.693 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=17 x-7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.199 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-5 y\\ y^{\prime }&=4 x-5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.291 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-2 y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=12 x-7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.962 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-5 y\\ y^{\prime }&=4 x-5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x\\ y^{\prime }&=-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=-3 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.287 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+3 y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
8.710 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+2 y+2 z\\ y^{\prime }&=x+4 y+z\\ z^{\prime }&=-2 x-4 y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.373 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y\\ y^{\prime }&=-x+2 y-z\\ z^{\prime }&=-y+3 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.488 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=z-x\\ z^{\prime }&=x+3 y+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.509 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x+4 y-4 z\\ y^{\prime }&=4 x-8 y-z\\ z^{\prime }&=-4 x-y-8 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y+z-w\\ y^{\prime }&=-y+2 z+2 w\\ z^{\prime }&=2 y+2 z+2 w\\ w^{\prime }&=-3 y-6 z-6 w\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.452 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+y\\ y^{\prime }&=x+3 y\\ z^{\prime }&=2 z+w+h\\ w^{\prime }&=z+2 w+h\\ h^{\prime }&=z+w+2 h\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.211 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-10 x+y+7 z\\ y^{\prime }&=-9 x+4 y+5 z\\ z^{\prime }&=-17 x+y+12 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
1.523 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=z\\ z^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.797 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+2 y+2 z\\ y^{\prime }&=x+4 y+z\\ z^{\prime }&=-2 x-4 y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.374 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y\\ y^{\prime }&=-x+2 y-z\\ z^{\prime }&=-y+3 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.400 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=z-x\\ z^{\prime }&=x+3 y+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.246 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x+4 y-4 z\\ y^{\prime }&=4 x-8 y-z\\ z^{\prime }&=-4 x-y-8 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.327 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-10 x+y+7 z\\ y^{\prime }&=-9 x+4 y+5 z\\ z^{\prime }&=-17 x+y+12 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.466 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=z\\ z^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.616 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=x-2 y\\ z^{\prime }&=x+y-5 z\\ u^{\prime }&=5 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.141 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=-x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=-x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y^{2}-x^{2}\\ y^{\prime }&=2 x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.041 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-\sin \left (x\right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-4 \sin \left (x\right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-x y\\ y^{\prime }&=-y+x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=-x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=\sin \left (x_{1}\right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=x_{1}-x_{1}^{3}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.042 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=a x+b y\\ y^{\prime }&=c x+d y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.793 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.861 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=-x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.002 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=5 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.028 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+4 y\\ y^{\prime }&=-2 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
8.730 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-6 y\\ y^{\prime }&=6 x-7 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+5 y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=4 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-6 y\\ y^{\prime }&=8 x-10 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-6 y+1\\ y^{\prime }&=6 x-7 y+1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-6 y+x y\\ y^{\prime }&=6 x-7 y-x y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.047 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y+\left (x^{2}+y^{2}\right )^{2}\\ y^{\prime }&=4 x-y+\left (x^{2}-y^{2}\right )^{5}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+x^{2}-x y\\ y^{\prime }&=-2 x+3 y+y^{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-x y\\ y^{\prime }&=-y+x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-x^{2}+y^{2}\\ y^{\prime }&=-y+2 x y\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.042 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x\\ y^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=-x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=-x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.968 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=-x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+6 y\\ y^{\prime }&=-7 x-9 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.963 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=2 y-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y-x^{2}+2 y^{2}\\ y^{\prime }&=3 x+2 y+x^{2} y^{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+x^{2}\\ y^{\prime }&=-3 y+x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.045 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+x y\\ y^{\prime }&=y+\left (x^{2}+y^{2}\right )^{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y^{2}\\ y^{\prime }&=3 y-x^{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.045 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-x y\\ y^{\prime }&=-y+x y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.042 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.284 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=2 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x-3 y\\ y^{\prime }&=-3 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.397 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+2 y\\ y^{\prime }&=-2 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x\\ y^{\prime }&=-x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+2 y\\ y^{\prime }&=-2 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.995 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-2\\ z^{\prime }&=x \,{\mathrm e}^{2 x +y}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&={\mathrm e}^{x}\\ z^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
8.336 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=z\\ z^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }&=-x\\ y z^{\prime }&=2\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.112 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 z&=y\\ z^{\prime }+4 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.303 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x +2 z\\ z^{\prime }&=3 x +y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2}+6 y+4 z\\ z^{\prime }&=y+3 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y+z+x\\ z^{\prime }&=1-y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=f \left (x \right )+a y+b z\\ z^{\prime }&=g \left (x \right )+c y+d z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
8.116 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=y\\ z^{\prime }&=3 y-x\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.042 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=z\\ z^{\prime }&=w\\ w^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
8.799 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x-y^{\prime }&=0\\ y^{\prime }+3 x-2 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x-y+z^{\prime }&=0\\ x^{\prime }-y&=1\\ y^{\prime }-y+z&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.876 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} v^{\prime }-2 v+2 w^{\prime }&=2-4 \,{\mathrm e}^{2 x}\\ 2 v^{\prime }-3 v+3 w^{\prime }-w&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.970 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-2 y-v^{\prime }-v&=6 \,{\mathrm e}^{3 x}\\ 2 y^{\prime }-3 y+v^{\prime }-3 v&=6 \,{\mathrm e}^{3 x}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
1.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y-v^{\prime }-v&=0\\ y^{\prime }+v^{\prime }-v&={\mathrm e}^{x}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 v^{\prime }+2 v+w^{\prime }-w&=3 x\\ v^{\prime }+v+w^{\prime }+w&=1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.805 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 v^{\prime }+2 v+w^{\prime }-6 w&=5 \,{\mathrm e}^{x}\\ 4 v^{\prime }+2 v+w^{\prime }-8 w&=5 \,{\mathrm e}^{x}+2 x -3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.130 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime }+2 y+w^{\prime }-w&=x +1\\ y^{\prime }+3 y+w^{\prime }+w&=4 x +14\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.723 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }-6 y_{1}&=-4 y_{2}\\ y_{2}^{\prime }&=2 y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }-3 y_{1}&=-4 y_{2}\\ y_{2}^{\prime }+y_{2}&=y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{2}\\ y_{2}^{\prime }&=-2 y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }-2 y_{1}&=2 y_{2}\\ y_{2}^{\prime \prime }+2 y_{2}^{\prime }+y_{2}&=-2 y_{1}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }+4 y_{1}&=10 y_{2}\\ y_{2}^{\prime \prime }-6 y_{2}^{\prime }+23 y_{2}&=9 y_{1}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.042 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }-2 y_{1}&=-2 y_{2}\\ y_{2}^{\prime \prime }+y_{2}^{\prime }+6 y_{2}&=4 y_{1}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime \prime }+2 y_{1}^{\prime }+6 y_{1}&=5 y_{2}\\ y_{2}^{\prime \prime }-2 y_{2}^{\prime }+6 y_{2}&=9 y_{1}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.062 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime \prime }+2 y_{1}&=-3 y_{2}\\ y_{2}^{\prime \prime }+2 y_{2}^{\prime }-9 y_{2}&=6 y_{1}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.050 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}\\ y_{2}^{\prime }&=y_{1} y_{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.034 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+y_{2}+t^{2}\\ y_{2}^{\prime }&=-y_{1}+y_{2}+1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\sin \left (t \right ) y_{1}\\ y_{2}^{\prime }&=y_{1}+\cos \left (t \right ) y_{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.027 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=t \sin \left (y_{1}\right )-y_{2}\\ y_{2}^{\prime }&=y_{1}+t \cos \left (y_{2}\right )\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.036 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}\\ y_{2}^{\prime }&=2 y_{1}+y_{4}\\ y_{3}^{\prime }&=y_{4}\\ y_{4}^{\prime }&=y_{2}+2 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.715 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {y_{1}}{2}-y_{2}+5\\ y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{2}-5\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=5 y_{1}-2 y_{2}\\ y_{2}^{\prime }&=4 y_{1}-y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}-y_{2}\\ y_{2}^{\prime }&=4 y_{1}-y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-y_{2}\\ y_{2}^{\prime }&=3 y_{1}-2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}+t\\ y_{2}^{\prime }&=-y_{1}-t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.778 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}\\ y_{2}^{\prime }&=3 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}\\ y_{2}^{\prime }&=-2 y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}+y_{2}\\ y_{2}^{\prime }&=2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.504 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}+2 y_{2}\\ y_{2}^{\prime }&=-2 y_{1}-y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-y_{2}\\ y_{2}^{\prime }&=3 y_{1}-2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.624 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-5 y_{2}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
4.470 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}-4 y_{2}\\ y_{2}^{\prime }&=y_{1}-y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}+3 y_{3}\\ y_{2}^{\prime }&=2 y_{2}\\ y_{3}^{\prime }&=y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{2}\\ y_{2}^{\prime }&=-y_{1}\\ y_{3}^{\prime }&=y_{1}+4 y_{2}-y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.277 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-y_{2}+{\mathrm e}^{t}\\ y_{2}^{\prime }&=3 y_{1}-2 y_{2}+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
4.712 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}+2 y_{2}+5\\ y_{2}^{\prime }&=-2 y_{1}-y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.171 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-5 y_{2}+2 \cos \left (t \right )\\ y_{2}^{\prime }&=y_{1}-2 y_{2}+\cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.647 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}-4 y_{2}+4\\ y_{2}^{\prime }&=y_{1}-y_{2}+1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}+y_{2}+{\mathrm e}^{t}\\ y_{2}^{\prime }&=y_{1}+2 y_{2}-{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
4.673 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=5 y_{1}+2 y_{2}+t\\ y_{2}^{\prime }&=-8 y_{1}-3 y_{2}-2 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.978 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-2 y_{1}+2 y_{2}+y_{3}+{\mathrm e}^{-2 t}\\ y_{2}^{\prime }&=-y_{2}\\ y_{3}^{\prime }&=2 y_{1}-2 y_{2}-y_{3}-{\mathrm e}^{-2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}+y_{3}+{\mathrm e}^{2 t}\\ y_{2}^{\prime }&=y_{1}+y_{2}-y_{3}+{\mathrm e}^{2 t}\\ y_{3}^{\prime }&=-2 y_{1}+y_{2}+3 y_{3}-{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.097 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-2 y_{1}+y_{2}\\ y_{2}^{\prime }&=-4 y_{1}+3 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=5 y_{1}-3 y_{2}\\ y_{2}^{\prime }&=2 y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2} t\\ y_{2}^{\prime }&=-y_{1} t\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1} t +y_{2} t\\ y_{2}^{\prime }&=-y_{1} t -y_{2} t\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {y_{1}}{t}+y_{2}\\ y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.028 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\left (2 t +1\right ) y_{1}+2 y_{2} t\\ y_{2}^{\prime }&=-2 y_{1} t +\left (1-2 t \right ) y_{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+y_{2}\\ y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {y_{2}}{t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {y_{1}}{t}+1\\ y_{2}^{\prime }&=\frac {y_{2}}{t}+t\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.028 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-\frac {y_{2}}{t}+1\\ y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {2 y_{2}}{t}-1\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {4 t y_{1}}{t^{2}+1}+\frac {6 y_{2} t}{t^{2}+1}-3 t\\ y_{2}^{\prime }&=-\frac {2 t y_{1}}{t^{2}+1}-\frac {4 y_{2} t}{t^{2}+1}+t\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.034 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 \sec \left (t \right ) y_{1}+5 \sec \left (t \right ) y_{2}\\ y_{2}^{\prime }&=-\sec \left (t \right ) y_{1}-3 \sec \left (t \right ) y_{2}\\ \end {array} \]
|
✗ |
✓ |
✗ |
✓ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1} t +y_{2} t +4 t\\ y_{2}^{\prime }&=-y_{1} t -y_{2} t +4 t\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 y\\ y^{\prime }&=5 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=4 y+{\mathrm e}^{t}\\ y^{\prime \prime }&=4 x-{\mathrm e}^{t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+2 y&=0\\ y^{\prime }+3 x-2 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }-x&=0\\ x^{\prime }+2 y^{\prime }&=4 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-y+2 z\\ z^{\prime }&=4 y+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=4 y-z\\ z^{\prime }&=2 y+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }+2 x-y&=-\sin \left (t \right )\\ x^{\prime }-3 x+y^{\prime }+2 y&=4 \cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.456 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y+5 y^{\prime }&=t\\ 2 y^{\prime }-x^{\prime \prime }+4 x&=2\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.058 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x\\ y^{\prime }&=2 x+3 y\\ z^{\prime }&=3 y-2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+6 y_{2}\\ y_{2}^{\prime }&=2 y_{1}-6 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}\\ y_{2}^{\prime }&=3 y_{1}-2 y_{2}\\ y_{3}^{\prime }&=2 y_{2}+3 y_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.100 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}\\ y_{2}^{\prime }&=-y_{1}+2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y+z-w\\ z^{\prime }&=y-z+w\\ w^{\prime }&=-y+z+w\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y-2 z\\ z^{\prime }&=4 y+5 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3 y-z\\ z^{\prime }&=y+3 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-2 z\\ z^{\prime }&=y+2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-3 y+z-w\\ z^{\prime }&=5 y-z-7 w\\ w^{\prime }&=-y+z-3 w\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.169 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3 y-4 z\\ z^{\prime }&=y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+y_{2}\\ y_{2}^{\prime }&=y_{1}-y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.878 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}-y_{2}\\ y_{2}^{\prime }&=y_{1}+2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x\\ y^{\prime }&=2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=y\\ y^{\prime \prime }&=x\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.016 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=x+y+t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.071 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {1}{y}\\ y^{\prime }&=\frac {1}{x}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.021 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=3 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x\\ y^{\prime }&=-2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=-5 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y+x \,y^{2}\\ y^{\prime }&=-7 x-2 y-7 y \,x^{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y+x^{2} y^{3}\\ y^{\prime }&=x-x^{3} y^{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+x^{3}\\ y^{\prime }&=x-y^{3}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+\sin \left (y\right )\\ y^{\prime }&=5 \,{\mathrm e}^{x}-5-y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.026 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y \cos \left (y\right )\\ y^{\prime }&=3 x-2 y-x \,y^{2}\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
0.026 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3-2 y\\ y^{\prime }&=2 x-2 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.178 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x+y&=0\\ y^{\prime }+y-x&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-\frac {y}{2}-3 t^{2}-\frac {t}{2}+\frac {3}{2}\\ y^{\prime }&=2 y-2 t -1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.119 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-7 x+y\\ y^{\prime }&=-2 x-5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.991 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-9 y\\ y^{\prime }&=x+8 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+z\\ y^{\prime }&=x+z\\ z^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.971 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+z\\ y^{\prime }&=3 x+z\\ z^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.263 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=8 y\\ y^{\prime }&=-2 z\\ z^{\prime }&=2 x+8 y-2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.512 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y-2 z+2-t\\ y^{\prime }&=1-x\\ z^{\prime }&=x+y-z+1-t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y+z+{\mathrm e}^{t}\\ y^{\prime }&=x-y+z+{\mathrm e}^{3 t}\\ z^{\prime }&=x+y+z+4\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.057 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x \cos \left (t \right )\\ 2 y^{\prime }&=\left ({\mathrm e}^{t}+{\mathrm e}^{-t}\right ) y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&={\mathrm e}^{t}-y-5 x\\ y^{\prime }&={\mathrm e}^{2 t}+x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+8 y\\ y^{\prime }&=-x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x-4 y\\ x^{\prime }+4 y^{\prime }&=-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-5 y\\ y^{\prime }&=x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.055 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y+t\\ y^{\prime }&=x-2 y+2 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+5 y\\ y^{\prime }&=-x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 y^{\prime }&=17 x+8 y\\ 13 x^{\prime }&=53 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.824 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ x^{\prime }-y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }&={\mathrm e}^{-t}-y\\ 2 x^{\prime }+y^{\prime }&=-2 y+\sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }&=6 x-y-6 t^{2}-t +3\\ y^{\prime }&=2 y-2 t -1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.962 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {1}{y}\\ y^{\prime }&=\frac {1}{x}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }&=t -2 x\\ y^{\prime } t&=t x+t y+2 x-t\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-13 y\\ y^{\prime }&=\frac {x}{4}-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-3 y\\ y^{\prime }&=x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.981 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+y\\ y^{\prime }&=-2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.964 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.886 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+3 y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.240 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x-y\\ y^{\prime }&=3 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.579 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+7 y\\ y^{\prime }&=2 x+5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+\frac {5 y}{7}\\ y^{\prime }&=7 x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x-y\\ y^{\prime }&=x-3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x\\ y^{\prime }&=3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+\alpha y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.202 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y-\sin \left (y\right )^{2}\\ y^{\prime }&=-x-3 y+x \left ({\mathrm e}^{\frac {x^{2}}{2}}-1\right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.116 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+3 y+x^{2} \sin \left (y\right )\\ y^{\prime }&=-x-4 y+1-\cos \left (y^{2}\right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+8 \sin \left (y\right )^{2}\\ y^{\prime }&=x-3 y+4 x^{3}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-22 \sin \left (y\right )+x^{2}-y^{3}\\ y^{\prime }&=\sin \left (x\right )-5 y+{\mathrm e}^{x^{2}}-1\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-10 x+4 \,{\mathrm e}^{y}-4 \cos \left (y^{2}\right )\\ y^{\prime }&=2 \,{\mathrm e}^{x}-2-y+x^{4}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.068 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x+2 \sin \left (y\right )-4 y^{4}\\ y^{\prime }&={\mathrm e}^{x}-3 y-1+\frac {5 x^{2}}{2}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.034 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-\frac {2 x}{3}+\frac {\sin \left (2 y\right )}{2}-x^{3} y\\ y^{\prime }&=-y-2 x+x^{4}-y^{7}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.034 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {5 x \,{\mathrm e}^{x}}{2}-3 y+\sin \left (x^{2}\right )\\ y^{\prime }&=2 x+y \,{\mathrm e}^{-\frac {y^{2}}{2}}-y^{4} \cos \left (x\right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.114 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {3 \sin \left (x\right )}{4}-7 y \left (1-y\right )^{{1}/{3}}+x^{3}\\ y^{\prime }&=\frac {2 x}{3}-3 y \cos \left (y\right )-11 y^{5}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\frac {{\mathrm e}^{x}}{4}-\frac {1}{4}-9 y+x^{4}\\ y^{\prime }&=\frac {x}{5}-\sin \left (y\right )+y^{14}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x+y \cos \left (y\right )-\frac {x^{3}}{3}\\ y^{\prime }&=3 x+2 y+\frac {x^{4}}{12}-y^{3} {\mathrm e}^{y}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}+3 x_{2}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+8 x_{2}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}\\ x_{2}^{\prime }&=4 x_{1}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.314 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-4 x_{2}+4 x_{3}\\ x_{2}^{\prime }&=12 x_{1}-11 x_{2}+12 x_{3}\\ x_{3}^{\prime }&=4 x_{1}-4 x_{2}+5 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}\\ x_{2}^{\prime }&=5 x_{1}-4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+2 x_{2}\\ x_{2}^{\prime }&=3 x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}\\ x_{2}^{\prime }&=x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}-2 x_{3}\\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}\\ x_{3}^{\prime }&=3 x_{1}-x_{2}-3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
15.931 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+2 x_{2}+x_{3}\\ x_{2}^{\prime }&=6 x_{1}-x_{2}\\ x_{3}^{\prime }&=-x_{1}-2 x_{2}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
114.564 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-4 x_{2}\\ x_{2}^{\prime }&=2 x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-2 x_{2}\\ x_{2}^{\prime }&=-6 x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.821 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-10 x_{2}\\ x_{2}^{\prime }&=-x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}\\ x_{3}^{\prime }&=x_{1}-x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.383 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}\\ x_{3}^{\prime }&=3 x_{1}+x_{2}-3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-4 x_{2}\\ x_{2}^{\prime }&=x_{1}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{2}\\ x_{2}^{\prime }&=-x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ x_{3}^{\prime }&=x_{1}-x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.421 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+x_{2}\\ x_{2}^{\prime }&=-5 x_{1}\\ x_{3}^{\prime }&=3 x_{2}-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.750 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}\\ x_{2}^{\prime }&=5 x_{1}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+2 x_{2}\\ x_{2}^{\prime }&=3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+5 x_{2}\\ x_{2}^{\prime }&=x_{2}\\ x_{3}^{\prime }&=4 x_{1}+8 x_{2}+x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.977 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+5 x_{2}+6 x_{3}\\ x_{2}^{\prime }&=8 x_{2}+9 x_{3}\\ x_{3}^{\prime }&=x_{2}-2 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.098 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=x_{3}\\ x_{3}^{\prime }&=x_{4}\\ x_{4}^{\prime }&=-x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
27.576 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+5 x_{2}-2 x_{3}+6 x_{4}\\ x_{2}^{\prime }&=3 x_{2}+4 x_{4}\\ x_{3}^{\prime }&=3 x_{2}+4 x_{4}\\ x_{4}^{\prime }&=x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.094 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}+2 x_{2}-3 \,{\mathrm e}^{t}\\ x_{2}^{\prime }&=-2 x_{1}+x_{2}+{\mathrm e}^{3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.193 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-4 x_{2}+1\\ x_{2}^{\prime }&=x_{1}-2 x_{2}+3 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=7 x_{1}-x_{2}+2 \,{\mathrm e}^{6 t}\\ x_{2}^{\prime }&=x_{1}+5 x_{2}+6 t \,{\mathrm e}^{6 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+{\mathrm e}^{2 t} \cos \left (3 t \right )\\ x_{2}^{\prime }&=6 x_{2}-4 x_{3}-2\\ x_{3}^{\prime }&=4 x_{2}-2 x_{3}-2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.849 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}-2 \,{\mathrm e}^{t}\\ x_{3}^{\prime }&=3 x_{3}\\ x_{4}^{\prime }&=-x_{1}+2 x_{2}+9 x_{3}+x_{4}+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+2\\ x_{2}^{\prime }&=5 x_{1}+2 x_{2}+10 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-4 x_{2}+2 \,{\mathrm e}^{t}\\ x_{2}^{\prime }&=4 x_{1}-3 x_{2}+2 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
1.055 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-3 x_{2}+x_{3}+10 \,{\mathrm e}^{2 t}\\ x_{2}^{\prime }&=2 x_{2}+4 x_{3}+6 \,{\mathrm e}^{2 t}\\ x_{3}^{\prime }&=x_{3}-{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.140 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-3 x_{2}+t \,{\mathrm e}^{-2 t}\\ x_{2}^{\prime }&=3 x_{1}-5 x_{2}+t \,{\mathrm e}^{-2 t}\\ x_{3}^{\prime }&=4 x_{1}+7 x_{2}-2 x_{3}+t^{2} {\mathrm e}^{-2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.196 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+x_{2}\\ x_{2}^{\prime }&=-4 x_{1}+3 x_{2}+10 \cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.620 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+3 x_{2}+8\\ x_{2}^{\prime }&=x_{1}+5 x_{2}+4 \,{\mathrm e}^{3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.595 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+6 \,{\mathrm e}^{3 t}\\ x_{2}^{\prime }&=x_{1}+x_{2}+4\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.114 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=6 x_{1}+5 x_{2}-4 \cos \left (3 t \right )\\ x_{2}^{\prime }&=x_{1}+2 x_{2}+8\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.213 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}+3 \,{\mathrm e}^{2 t}\\ x_{2}^{\prime }&=9 x_{1}-3 x_{2}+{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.438 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+6 \,{\mathrm e}^{2 t}\\ x_{2}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.075 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-2 x_{2}+2 t\\ x_{2}^{\prime }&=-x_{1}+2 x_{2}+5\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-5 x_{2}+5 \sin \left (t \right )\\ x_{2}^{\prime }&=x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.429 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-4 x_{2}+3 x_{3}-3 \,{\mathrm e}^{-3 t}\\ x_{2}^{\prime }&=12 x_{1}-11 x_{2}+12 x_{3}+t\\ x_{3}^{\prime }&=4 x_{1}-4 x_{2}+5 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.244 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-x_{2}-x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}+t\\ x_{3}^{\prime }&=x_{1}-x_{2}+x_{3}+2 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.819 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}-x_{1}\\ x_{2}^{\prime }&=-5 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+x_{2}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=4 x_{1}+8 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.421 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-x_{2}\\ x_{2}^{\prime }&=2 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{3}\\ x_{2}^{\prime }&=-2 x_{1}+x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.885 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-5 x_{2}\\ x_{2}^{\prime }&=5 x_{1}-7 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+4 x_{2}\\ x_{2}^{\prime }&=3 x_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=9 x_{1}-7 x_{2}\\ x_{2}^{\prime }&=6 x_{1}-4 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.805 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=7 x_{1}-17 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.138 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-7 x_{2}\\ x_{2}^{\prime }&=5 x_{1}-10 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.863 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}-x_{2}\\ x_{2}^{\prime }&=x_{1}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-5 x_{2}\\ x_{2}^{\prime }&=8 x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.064 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}-x_{2}\\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.963 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-6 x_{1}-7 x_{2}\\ x_{2}^{\prime }&=7 x_{1}-20 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-\frac {x y}{2}\\ y^{\prime }&=2 x y-\frac {6 y}{5}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.024 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=3 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y\\ y^{\prime }&=-4 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x-8 y&=0\\ -x+y^{\prime }-y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=-2 x+3 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-3 y\\ y^{\prime }&=3 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x+5 y&=0\\ -x+y^{\prime }-y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=-x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y\\ y^{\prime }&=4 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.852 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 x+2 y\\ y^{\prime }&=-2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-5 x-3 y&=0\\ 3 x+y^{\prime }+y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y+z\\ y^{\prime }&=x+y-z\\ z^{\prime }&=2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y-z\\ y^{\prime }&=y+z-x\\ z^{\prime }&=x-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.670 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y+z\\ y^{\prime }&=x+2 y-z\\ z^{\prime }&=x-y+2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-y+z\\ y^{\prime }&=x+y+z\\ z^{\prime }&=4 x-y+4 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 y-2 z-3 x\\ y^{\prime }&=x+z\\ z^{\prime }&=6 x-6 y+5 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y-z\\ y^{\prime }&=x+y\\ z^{\prime }&=3 x+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.228 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=x+3 y-z\\ z^{\prime }&=2 y+3 z-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y+2 z\\ y^{\prime }&=x+2 z\\ z^{\prime }&=-2 x+y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-y-z\\ y^{\prime }&=x+2 y-z\\ z^{\prime }&=x-y+2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y-z\\ y^{\prime }&=3 x-2 y-3 z\\ z^{\prime }&=-x+y+2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y-2 x-2 z\\ y^{\prime }&=x-2 y+2 z\\ z^{\prime }&=2 x-3 y+5 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.222 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y-z\\ y^{\prime }&=3 x-4 y-3 z\\ z^{\prime }&=2 x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.689 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y+z\\ y^{\prime }&=x+y-z\\ z^{\prime }&=-y+2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.104 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y-2 z-x\\ y^{\prime }&=4 x+y\\ z^{\prime }&=2 x+y-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=2 y+4 z\\ z^{\prime }&=x-z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y-z\\ y^{\prime }&=2 x-y-2 z\\ z^{\prime }&=-x+y+2 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-y\\ y^{\prime }&=3 x+y-z\\ z^{\prime }&=x+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=2 x-3 y\\ y^{\prime \prime }&=x-2 y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=3 x+4 y\\ y^{\prime \prime }&=-x-y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.024 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=2 y\\ y^{\prime \prime }&=-2 x\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=3 x-y-z\\ y^{\prime \prime }&=-x+3 y-z\\ z^{\prime \prime }&=-x-y+3 z\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }-5 y^{\prime }&=-x+4 y\\ 3 x^{\prime }-4 y^{\prime }&=2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=0\\ x^{\prime }+x-y^{\prime }&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.052 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-2 y^{\prime \prime }+y^{\prime }+x-3 y&=0\\ 4 y^{\prime \prime }-2 x^{\prime \prime }-x^{\prime }-2 x+5 y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x+2 y^{\prime \prime }-2 y&=0\\ x^{\prime }-x+y^{\prime }+y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.026 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 x-2 y^{\prime }&=0\\ 3 x^{\prime }+y^{\prime \prime }-8 y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+3 y^{\prime \prime }-x&=0\\ x^{\prime }+3 y^{\prime }-2 y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+5 x^{\prime }+2 y^{\prime }+y&=0\\ 3 x^{\prime \prime }+5 x+y^{\prime }+3 y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.029 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }-2 x-2 y^{\prime }-y&=0\\ x^{\prime \prime }-4 x^{\prime }-y^{\prime \prime }+2 y^{\prime }+2 y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.036 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime \prime }+2 x^{\prime }+x+3 y^{\prime \prime }+y^{\prime }+y&=0\\ x^{\prime \prime }+4 x^{\prime }-x+3 y^{\prime \prime }+2 y^{\prime }-y&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.034 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+2 \,{\mathrm e}^{t}\\ y^{\prime }&=x+t^{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y-5 \cos \left (t \right )\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+2 y+4 \,{\mathrm e}^{5 t}\\ y^{\prime }&=x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.115 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-4 y+{\mathrm e}^{-2 t}\\ y^{\prime }&=x-2 y-3 \,{\mathrm e}^{-2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x+y-2 \,{\mathrm e}^{2 t}\\ y^{\prime }&=-2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x+1\\ y^{\prime }&=8 y-2 x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
1.160 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5 x-3 y+2 \,{\mathrm e}^{3 t}\\ y^{\prime }&=x+y+5 \,{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y+1+{\mathrm e}^{t}\\ y^{\prime }&=3 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=x-5 \sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-4 y\\ y^{\prime }&=x-3 y+3 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=y-2 x+18 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.154 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y+16 \,{\mathrm e}^{t} t\\ y^{\prime }&=2 x-2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+4 y-8\\ y^{\prime }&=3 x+6 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-3 y\\ y^{\prime }&=x-2 y+2 \sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+3 y+5 t\\ y^{\prime }&=3 x+2 y+8 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=x+2 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 x-3 y+\sin \left (t \right )\\ y^{\prime }&=2 x-y-2 \cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y+2 \,{\mathrm e}^{t}\\ y^{\prime }&=x+2 y-3 \,{\mathrm e}^{4 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-4 y+8 t\\ y^{\prime }&=5 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.754 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=2 y-x-5 \,{\mathrm e}^{t} \sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+\tan \left (t \right )^{2}-1\\ y^{\prime }&=\tan \left (t \right )-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.970 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y-x\\ y^{\prime }&=4 y-3 x+\frac {{\mathrm e}^{3 t}}{1+{\mathrm e}^{2 t}}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.018 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1}\\ y^{\prime }&=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y+\frac {1}{\cos \left (t \right )}\\ y^{\prime }&=2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=2 x-y+15 \,{\mathrm e}^{t} \sqrt {t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.565 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x y-x+y\\ y^{\prime }&=5 x^{4}+y^{3}+2 x-3 y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x^{2}+y^{2}-2 x\\ y^{\prime }&=3 x^{2}-x+3 y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.021 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&={\mathrm e}^{x+2 y}-3 \cos \left (3 x\right )\\ y^{\prime }&=2 \sqrt {1+2 x}-2 \,{\mathrm e}^{y}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.024 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\ln \left (4 y+{\mathrm e}^{-3 x}\right )\\ y^{\prime }&=2 y-1+\left (1-6 x\right )^{{1}/{3}}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.021 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y-x^{2}-x\\ y^{\prime }&=3 x-x^{2}-y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.021 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\left (x-1\right ) \left (y-1\right )\\ y^{\prime }&=x y-2\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.018 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=5-x^{2}-y^{2}\\ y^{\prime }&=1+y^{2}-x\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=\sin \left (x+y\right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\ln \left (1+2 t -2 x\right )+3 y+3 t^{2}+1\\ y^{\prime }&=x^{2}-2 t x-2 x-y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.022 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x^{3}-y\\ y^{\prime }&=x+y^{3}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y-x+x y\\ y^{\prime }&=x-y-x^{2}-y^{3}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.022 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 y^{3}-x^{5}\\ y^{\prime }&=-x-y^{3}+y^{5}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y-3 x-x^{3}\\ y^{\prime }&=6 x-2 y\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
0.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
3.152 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+2 y\\ y^{\prime }&=-2 x+5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.337 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 y\\ y^{\prime }&=-6 x-5 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x\\ y^{\prime }&=2 x-y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x-5 y\\ y^{\prime }&=2 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.784 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x+y\\ y^{\prime }&=-x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=-6 x+4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-2 x+y\\ y^{\prime }&=-4 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x-y\\ y^{\prime }&=x-3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y-1\\ y^{\prime }&=x-y-3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x}{z}\\ z^{\prime }&=-\frac {x}{y}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.022 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y^{2}}{z-x}\\ z^{\prime }&=1+y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.021 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {z}{x}\\ z^{\prime }&=\frac {z \left (y+2 z-1\right )}{x \left (-1+y\right )}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{2} z\\ z^{\prime }&=\frac {z}{x}-y \,z^{2}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 z y^{\prime }&=y^{2}-z^{2}+1\\ z^{\prime }&=z+y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=z\\ z^{\prime }&=-y\\ \end {array} \]
|
✓ |
✓ |
✗ |
✓ |
0.354 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -x^{\prime }+y^{\prime }+z^{\prime }-x+2 z&={\mathrm e}^{-t}\\ x^{\prime }-y^{\prime }+z^{\prime }+x&=2 \,{\mathrm e}^{-t}\\ x^{\prime }+y^{\prime }-z^{\prime }+x+2 y&=3 \,{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.856 |
|