| # |
ODE |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-3 x_{2}\\ x_{2}^{\prime }&=-2 x_{1}+2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-x_{2}\\ x_{2}^{\prime }&=5 x_{1}-3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}+t\\ x_{2}^{\prime }&=2 x_{1}-2 x_{2}+3 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{t}\\ x_{2}^{\prime }&=4 x_{1}+x_{2}-{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-4 x_{2}+{\mathrm e}^{t}\\ x_{2}^{\prime }&=x_{1}-x_{2}+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-5 x_{2}+\sin \left (t \right )\\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\tan \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
497.906 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right )\\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}+f_{1} \left (t \right )\\ x_{2}^{\prime }&=-x_{1}+f_{2} \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
5.426 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}+\delta \left (t -\pi \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1-\operatorname {Heaviside}\left (t -\pi \right )\\ x_{2}^{\prime }&=2 x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}-3 x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{2}+2 x_{3}\\ x_{3}^{\prime }&=x_{1}-x_{2}+4 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{3}+{\mathrm e}^{2 t}\\ x_{2}^{\prime }&=2 x_{2}\\ x_{3}^{\prime }&=3 x_{3}+{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-x_{2}+2 x_{3}+{\mathrm e}^{t}\\ x_{2}^{\prime }&=x_{1}+x_{2}+x_{3}\\ x_{3}^{\prime }&=2 x_{1}+x_{2}+3 x_{3}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
1.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3}\\ x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3}+{\mathrm e}^{t} \cos \left (2 t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}\\ x_{3}^{\prime }&=3 x_{3}\\ x_{4}^{\prime }&=2 x_{3}+3 x_{4}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x-2 y&=16 \,{\mathrm e}^{t} t\\ 2 x-y^{\prime }-2 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.485 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 x+y&=5 \,{\mathrm e}^{t} \cos \left (t \right )\\ x+y^{\prime }-2 y&=10 \,{\mathrm e}^{t} \sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.165 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-4 x+3 y&=\sin \left (t \right )\\ 2 x+y^{\prime }-y&=2 \cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t}\\ x-y^{\prime }+2 y&=3 \,{\mathrm e}^{4 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=40 \,{\mathrm e}^{3 t}\\ x^{\prime }+x-y^{\prime }&=36 \,{\mathrm e}^{t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t}\\ y^{\prime }-2 y-4 z&=4 \,{\mathrm e}^{2 t}\\ x-z^{\prime }-z&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 x-2 y^{\prime }&=0\\ 3 x^{\prime }+y^{\prime \prime }-8 y&=240 \,{\mathrm e}^{t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.036 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x-2 y&=0\\ x-y^{\prime }&=15 \cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.187 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+y&=2 \sin \left (t \right ) \left (1-\operatorname {Heaviside}\left (t -\pi \right )\right )\\ 2 x-y^{\prime }-y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+x-5 y^{\prime }-4 y&=28 \,{\mathrm e}^{t} \operatorname {Heaviside}\left (-2+t \right )\\ 3 x^{\prime }-2 x-4 y^{\prime }+y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.256 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }+x&=0\\ x^{\prime }-x+2 y^{\prime }&={\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.692 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-5 y_{1}+y_{2}\\ y_{2}^{\prime }&=-9 y_{1}+5 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=5 y_{1}-2 y_{2}\\ y_{2}^{\prime }&=6 y_{1}-2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}-4 y_{2}\\ y_{2}^{\prime }&=5 y_{1}-4 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=6 y_{2}\\ y_{2}^{\prime }&=-6 y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-4 y_{1}-y_{2}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-64 y_{2}\\ y_{2}^{\prime }&=y_{1}-14 y_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-4 y_{1}-y_{2}+2 \,{\mathrm e}^{t}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (2 t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=5 y_{1}-y_{2}+{\mathrm e}^{-t}\\ y_{2}^{\prime }&=y_{1}+3 y_{2}+2 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}-5 y_{2}+3\\ y_{2}^{\prime }&=y_{1}+3 y_{2}+5 \cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-2 y_{1}+y_{2}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{2}-y_{3}\\ y_{2}^{\prime }&=y_{1}+y_{3}-{\mathrm e}^{-t}\\ y_{3}^{\prime }&=y_{1}+y_{2}+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-4 x_{1}-x_{2}\\ x_{2}^{\prime }&=x_{1}-2 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.557 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-x_{2}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}-x_{3}\\ x_{2}^{\prime }&=x_{1}+x_{3}\\ x_{3}^{\prime }&=x_{1}+x_{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.873 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+3 y+2 \sin \left (2 t \right )\\ y^{\prime }&=-3 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-4 x-y+{\mathrm e}^{-t}\\ y^{\prime }&=x-2 y+2 \,{\mathrm e}^{-3 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.155 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-y+2 \cos \left (t \right )\\ y^{\prime }&=x+y+3 \sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.156 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y\\ y^{\prime }&=-x-4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.493 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+y\\ y^{\prime }&=x+y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.428 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=-y+\delta \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.477 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-6 x+3 y&=8 \,{\mathrm e}^{t}\\ y^{\prime }-2 x-y&=4 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.541 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+z&=t\\ z^{\prime }+4 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime }+y&=\sin \left (t \right )\\ y^{\prime }-z&={\mathrm e}^{t}\\ w+y+z^{\prime }&=1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.709 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+z&=t\\ z^{\prime }+4 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime }+y&=\sin \left (t \right )\\ y^{\prime }-z&={\mathrm e}^{t}\\ w+y+z^{\prime }&=1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
1.485 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+z+y&=0\\ y^{\prime }+z^{\prime }&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime \prime }+y^{\prime }&=\cos \left (t \right )\\ y^{\prime \prime }-z&=\sin \left (t \right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.056 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime \prime }-y+2 z&=3 \,{\mathrm e}^{-t}\\ -2 w^{\prime }+2 y^{\prime }+z&=0\\ 2 w^{\prime }-2 y+z^{\prime }+2 z^{\prime \prime }&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.086 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+z&=t\\ z^{\prime }-y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-z&=0\\ y-z^{\prime }&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime }-w-2 y&=1\\ y^{\prime }-4 w-3 y&=-1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime }-y&=0\\ w+y^{\prime }+z&=1\\ w-y+z^{\prime }&=2 \sin \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
1.390 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }-2 v&=2\\ u+v^{\prime }&=5 \,{\mathrm e}^{2 t}+1\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime \prime }-2 z&=0\\ w^{\prime }+y^{\prime }-z&=2 t\\ w^{\prime }-2 y+z^{\prime \prime }&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.075 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} w^{\prime \prime }+y+z&=-1\\ w+y^{\prime \prime }-z&=0\\ -w-y^{\prime }+z^{\prime \prime }&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.075 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y\\ y^{\prime }&=-x\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x-5 y&=0\\ y^{\prime }+4 x+5 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.229 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 y^{\prime }+y&={\mathrm e}^{t}\\ -x+y^{\prime }&=y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-3 x-6 y&=27 t^{2}\\ x^{\prime }+y^{\prime }-3 y&=5 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.291 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=-2 y\\ y^{\prime }&=y-x^{\prime }\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.034 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=x-2\\ x^{\prime \prime }&=2+y\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }&=\cos \left (t \right )\\ x+y^{\prime \prime }&=2\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=x-y\\ z^{\prime }&=2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.367 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y+z\\ y^{\prime }&=2 x+5 y+3 z\\ z^{\prime }&=3 x+9 y+5 z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.462 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=y+4 \,{\mathrm e}^{-2 t}\\ y^{\prime \prime }&=x-{\mathrm e}^{-2 t}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.035 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y&=4\\ x-y^{\prime }&=3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.692 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+y^{\prime \prime }&=t\\ x^{\prime \prime }-y^{\prime \prime }&=3 t\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{\prime }-2 y&=\cos \left (2 t \right )\\ x-2 y^{\prime }&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{-3 t}\\ 5 x+y^{\prime }+3 y&=5 \,{\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{\prime }+2 y^{\prime }+3 x&=E \sin \left (t \right )\\ 4 x+2 x^{\prime }+3 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{2}\\ y_{2}^{\prime }-2 y_{2}&=y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }-y_{1}&=-2 y_{2}\\ y_{2}^{\prime }-y_{2}&=2 y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }-2 y_{1}&=-y_{2}\\ y_{2}^{\prime \prime }-y_{2}^{\prime }+y_{2}&=y_{1}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }+2 y_{1}&=5 y_{2}\\ y_{2}^{\prime \prime }-2 y_{2}^{\prime }+5 y_{2}&=2 y_{1}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.045 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime \prime }+2 y_{1}&=-3 y_{2}\\ y_{2}^{\prime \prime }+2 y_{2}^{\prime }-9 y_{2}&=6 y_{1}\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y&=3 \,{\mathrm e}^{2 t}\\ x+y^{\prime }&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.133 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+y^{\prime }&=2\\ x^{\prime \prime }-y^{\prime \prime }&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
0.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y&=0\\ x+y^{\prime }&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x-2 y&=0\\ y^{\prime }+x+4 y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-y\\ y^{\prime }&=2 x+2 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 y&=3 t\\ y^{\prime }-2 x&=4\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x&=y+{\mathrm e}^{t}\\ y+y^{\prime }&=x+{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }&=y+{\mathrm e}^{t}\\ 2 x^{\prime }+y^{\prime }+2 y&=\cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y-z\\ y^{\prime }&=x+y\\ z^{\prime }&=x+z\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 y+z\\ y^{\prime }&=z\\ z^{\prime }&=4 y\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.904 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 y^{\prime }+x+y+z&=0\\ x^{\prime }+y^{\prime }+x+z&=0\\ z^{\prime }+2 y^{\prime }-y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-2 y^{\prime }&=1\\ x^{\prime }-x+y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }-3 y+y^{\prime }&=0\\ x^{\prime }+y^{\prime }&=t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.112 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 y^{\prime }-y&=1\\ 2 x^{\prime }+y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }-x&=\cos \left (t \right )\\ x^{\prime }+2 y^{\prime }&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.129 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{\prime }-y&=2 t\\ x^{\prime }+y^{\prime }-y&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+4 y^{\prime }-y&=0\\ x^{\prime }+2 y&={\mathrm e}^{-t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.122 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+2 x-y^{\prime }&=0\\ x^{\prime }+x+y&=t^{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
0.118 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+4 x-y&=0\\ x^{\prime }+y^{\prime }&=t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.143 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+y^{\prime }+x-y&=0\\ x^{\prime }+2 y^{\prime }+x&=1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.107 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+2 y^{\prime }&=0\\ 4 x^{\prime }+3 y^{\prime }+y&=-6\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.126 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }-2 y_{2}^{\prime }+3 y_{1}&=0\\ y_{1}-4 y_{2}^{\prime }+3 y_{3}&=t\\ y_{1}-2 y_{2}^{\prime }+3 y_{3}^{\prime }&=-1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
0.262 |
|