| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=x \,{\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=72 x^{5} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.351 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.342 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{4} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.362 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y&=8 x^{{4}/{3}} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.172 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.763 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{2}-1 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.608 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+9 x&=10 \cos \left (2 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.431 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x&=5 \sin \left (3 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.135 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right )\\ x \left (0\right )&=375\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.213 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+25 x&=90 \cos \left (4 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=90\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.161 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+4 x&=10 \cos \left (3 t \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.914 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+3 x^{\prime }+5 x&=-4 \cos \left (5 t \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime \prime }+2 x^{\prime }+x&=3 \sin \left (10 t \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+3 x^{\prime }+3 x&=8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.362 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.974 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 x^{\prime }+26 x&=600 \cos \left (10 t \right )\\ x \left (0\right )&=10\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.672 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+8 x^{\prime }+25 x&=200 \cos \left (t \right )+520 \sin \left (t \right )\\ x \left (0\right )&=-30\\ x^{\prime }\left (0\right )&=-10\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.485 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-3 y\\ y^{\prime }&=3 x\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=3 x-2 y\\ y^{\prime }&=2 x+y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.506 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t}\\ y^{\prime }&=5 x-y-t^{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
4.329 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=y+z\\ y^{\prime }&=x+z\\ z^{\prime }&=x+y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}\\ x_{2}^{\prime }&=2 x_{3}\\ x_{3}^{\prime }&=3 x_{4}\\ x_{4}^{\prime }&=4 x_{1}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
5.155 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{2}+x_{3}+1\\ x_{2}^{\prime }&=x_{3}+x_{4}+t\\ x_{3}^{\prime }&=x_{1}+x_{4}+t^{2}\\ x_{4}^{\prime }&=x_{1}+x_{2}+t^{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
5.739 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.157 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.145 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.174 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right ) y^{\prime \prime }-\left (2+x \right ) y^{\prime }+y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.134 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \end {array} \]
|
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.142 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \end {array} \]
|
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.167 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.082 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.082 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.100 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.072 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.079 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-16 y^{\prime \prime }+16 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.118 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.097 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }&=16 y \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.072 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.069 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.120 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }-2 y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ y^{\prime \prime }\left (0\right )&=3\\ \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.282 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime \prime \prime }+2 y^{\prime \prime }&=0\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=1\\ \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime }&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=4\\ y^{\prime \prime }\left (0\right )&=5\\ \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+27 y&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.062 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.094 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.079 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.088 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=10\\ y^{\prime \prime }\left (0\right )&=250\\ \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.185 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }&=y\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.299 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }&=y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+2 y\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=15\\ \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.251 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x&=0 \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.304 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+y^{\prime } x&=0 \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x&=0 \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.208 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+y^{\prime } x&=0 \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y&=0 \end {array} \]
|
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=6 x_{1}\\ x_{2}^{\prime }&=-3 x_{1}-x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+2 x_{2}\\ x_{2}^{\prime }&=-3 x_{1}+4 x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+3 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+4 x_{2}\\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.593 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}\\ x_{2}^{\prime }&=6 x_{1}-x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=6 x_{1}-7 x_{2}\\ x_{2}^{\prime }&=x_{1}-2 x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=9 x_{1}+5 x_{2}\\ x_{2}^{\prime }&=-6 x_{1}-2 x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}+4 x_{2}\\ x_{2}^{\prime }&=6 x_{1}-5 x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}-x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.642 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}-5 x_{2}\\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-3 x_{1}-2 x_{2}\\ x_{2}^{\prime }&=9 x_{1}+3 x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-2 x_{2}\\ x_{2}^{\prime }&=2 x_{1}+x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}-5 x_{2}\\ x_{2}^{\prime }&=x_{1}+3 x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-9 x_{2}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.905 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}-4 x_{2}\\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=7 x_{1}-5 x_{2}\\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.876 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-50 x_{1}+20 x_{2}\\ x_{2}^{\prime }&=100 x_{1}-60 x_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}+4 x_{3}\\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3}\\ x_{3}^{\prime }&=4 x_{1}+x_{2}+4 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.981 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}+2 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=2 x_{1}+7 x_{2}+x_{3}\\ x_{3}^{\prime }&=2 x_{1}+x_{2}+7 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=x_{1}+4 x_{2}+x_{3}\\ x_{3}^{\prime }&=x_{1}+x_{2}+4 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}+x_{2}+3 x_{3}\\ x_{2}^{\prime }&=x_{1}+7 x_{2}+x_{3}\\ x_{3}^{\prime }&=3 x_{1}+x_{2}+5 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
3.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}-6 x_{3}\\ x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3}\\ x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=-5 x_{1}-4 x_{2}-2 x_{3}\\ x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+x_{2}+x_{3}\\ x_{2}^{\prime }&=-5 x_{1}-3 x_{2}-x_{3}\\ x_{3}^{\prime }&=5 x_{1}+5 x_{2}+3 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3}\\ x_{2}^{\prime }&=-4 x_{1}-3 x_{2}-x_{3}\\ x_{3}^{\prime }&=4 x_{1}+4 x_{2}+2 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.342 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3}\\ x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3}\\ x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
3.349 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=3 x_{1}+x_{3}\\ x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3}\\ x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.804 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=x_{1}\\ x_{2}^{\prime }&=2 x_{1}+2 x_{2}\\ x_{3}^{\prime }&=3 x_{2}+3 x_{3}\\ x_{4}^{\prime }&=4 x_{3}+4 x_{4}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
3.463 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-2 x_{1}+9 x_{4}\\ x_{2}^{\prime }&=4 x_{1}+2 x_{2}-10 x_{4}\\ x_{3}^{\prime }&=-x_{3}+8 x_{4}\\ x_{4}^{\prime }&=x_{4}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.657 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=2 x_{1}\\ x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4}\\ x_{3}^{\prime }&=5 x_{3}\\ x_{4}^{\prime }&=-21 x_{3}-2 x_{4}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
3.868 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4}\\ x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4}\\ x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4}\\ x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
3.710 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-40 x_{1}-12 x_{2}+54 x_{3}\\ x_{2}^{\prime }&=35 x_{1}+13 x_{2}-46 x_{3}\\ x_{3}^{\prime }&=-25 x_{1}-7 x_{2}+34 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=-20 x_{1}+11 x_{2}+13 x_{3}\\ x_{2}^{\prime }&=12 x_{1}-x_{2}-7 x_{3}\\ x_{3}^{\prime }&=-48 x_{1}+21 x_{2}+31 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
3.290 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=147 x_{1}+23 x_{2}-202 x_{3}\\ x_{2}^{\prime }&=-90 x_{1}-9 x_{2}+129 x_{3}\\ x_{3}^{\prime }&=90 x_{1}+15 x_{2}-123 x_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.226 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=9 x_{1}-7 x_{2}-5 x_{3}\\ x_{2}^{\prime }&=-12 x_{1}+7 x_{2}+11 x_{3}+9 x_{4}\\ x_{3}^{\prime }&=24 x_{1}-17 x_{2}-19 x_{3}-9 x_{4}\\ x_{4}^{\prime }&=-18 x_{1}+13 x_{2}+17 x_{3}+9 x_{4}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
5.849 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=13 x_{1}-42 x_{2}+106 x_{3}+139 x_{4}\\ x_{2}^{\prime }&=2 x_{1}-16 x_{2}+52 x_{3}+70 x_{4}\\ x_{3}^{\prime }&=x_{1}+6 x_{2}-20 x_{3}-31 x_{4}\\ x_{4}^{\prime }&=-x_{1}-6 x_{2}+22 x_{3}+33 x_{4}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.496 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x_{1}^{\prime }&=23 x_{1}-18 x_{2}-16 x_{3}\\ x_{2}^{\prime }&=-8 x_{1}+6 x_{2}+7 x_{3}+9 x_{4}\\ x_{3}^{\prime }&=34 x_{1}-27 x_{2}-26 x_{3}-9 x_{4}\\ x_{4}^{\prime }&=-26 x_{1}+21 x_{2}+25 x_{3}+12 x_{4}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
6.062 |
|