| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y&=-{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.160 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y&=2 \,{\mathrm e}^{x} \left (x +1\right )+{\mathrm e}^{-2 x} \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.264 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+4 y&=\sinh \left (x \right ) \cos \left (x \right )-\cosh \left (x \right ) \sin \left (x \right ) \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.341 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y&={\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x} \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.285 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y&={\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right ) \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&={\mathrm e}^{2 x} \left (10+3 x \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime \prime }-2 y&=-{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.230 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=-2 \,{\mathrm e}^{-x} \left (6 x^{2}-18 x +7\right ) \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \left (x +1\right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.166 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=-{\mathrm e}^{-x} \left (3 x^{2}-9 x +4\right ) \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.227 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \left (x \right )+\left (8-9 x \right ) \sin \left (x \right )\right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.271 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right ) \end {array} \]
|
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.275 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&={\mathrm e}^{x} \left (\left (2+6 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.805 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{x} \left (1-6 x \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=7\\ y^{\prime \prime }\left (0\right )&=9\\ \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=-{\mathrm e}^{-x} \left (4-8 x \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime \prime }-3 y^{\prime }-y&={\mathrm e}^{-\frac {x}{2}} \left (2-3 x \right )\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=15\\ y^{\prime \prime }\left (0\right )&=-17\\ \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.367 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-x} \left (20-12 x \right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-4\\ y^{\prime \prime }\left (0\right )&=7\\ y^{\prime \prime \prime }\left (0\right )&=-22\\ \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y&=30 \cos \left (x \right )-10 \sin \left (x \right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-4\\ y^{\prime \prime }\left (0\right )&=16\\ \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.250 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+5 y^{\prime \prime }-2 y^{\prime }&=-2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-1\\ y^{\prime \prime \prime }\left (0\right )&=-5\\ \end {array} \]
|
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
6.716 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=2 x \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.371 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 y^{\prime } x +2 y&=30 x^{2} \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{2} \end {array} \]
|
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.458 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 y^{\prime } x +9 y&=96 x^{{5}/{2}} \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 y^{\prime } x +24 y&=x^{4} \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.476 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=12 x^{2} \end {array} \]
|
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.460 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=4 x\\ y \left (1\right )&=4\\ y^{\prime }\left (1\right )&=4\\ y^{\prime \prime }\left (1\right )&=2\\ \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y&=x^{3}\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=1\\ y^{\prime \prime }\left (1\right )&=7\\ \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.534 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 y^{\prime } x -16 y&=9 x^{4}\\ y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=1\\ y^{\prime \prime }\left (1\right )&=5\\ \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \left (x +1\right )\\ y \left (-1\right )&=-6\\ y^{\prime }\left (-1\right )&={\frac {43}{6}}\\ y^{\prime \prime }\left (-1\right )&=-{\frac {5}{2}}\\ \end {array} \]
|
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=9 x^{2}\\ y \left (1\right )&=-7\\ y^{\prime }\left (1\right )&=-11\\ y^{\prime \prime }\left (1\right )&=-5\\ y^{\prime \prime \prime }\left (1\right )&=6\\ \end {array} \]
|
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.774 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-y^{\prime } x +y&=6 x\\ y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=0\\ y^{\prime \prime }\left (1\right )&=4\\ y^{\prime \prime \prime }\left (1\right )&=-{\frac {37}{4}}\\ \end {array} \]
|
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y&=40 x^{3}\\ y \left (-1\right )&=-1\\ y^{\prime }\left (-1\right )&=-7\\ y^{\prime \prime }\left (-1\right )&=-1\\ y^{\prime \prime \prime }\left (-1\right )&=-31\\ \end {array} \]
|
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=F \left (x \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=F \left (x \right ) \end {array} \]
|
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.372 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=F \left (x \right ) \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=F \left (x \right ) \end {array} \]
|
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+2 y_{2}\\ y_{2}^{\prime }&=2 y_{1}+y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.479 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-\frac {5 y_{1}}{4}+\frac {3 y_{2}}{4}\\ y_{2}^{\prime }&=\frac {3 y_{1}}{4}-\frac {5 y_{2}}{4}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-\frac {4 y_{1}}{5}+\frac {3 y_{2}}{5}\\ y_{2}^{\prime }&=-\frac {2 y_{1}}{5}-\frac {11 y_{2}}{5}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.547 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}-4 y_{2}\\ y_{2}^{\prime }&=-y_{1}-y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.529 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}-4 y_{2}\\ y_{2}^{\prime }&=-y_{1}-y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}-3 y_{2}\\ y_{2}^{\prime }&=2 y_{1}-y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.522 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-6 y_{1}-3 y_{2}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}-y_{2}-2 y_{3}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}-3 y_{3}\\ y_{3}^{\prime }&=-4 y_{1}+y_{2}-y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.136 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-8 y_{3}\\ y_{2}^{\prime }&=-4 y_{1}-4 y_{3}\\ y_{3}^{\prime }&=-8 y_{1}-4 y_{2}-6 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.878 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+5 y_{2}+8 y_{3}\\ y_{2}^{\prime }&=y_{1}-y_{2}-2 y_{3}\\ y_{3}^{\prime }&=-y_{1}-y_{2}-y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.990 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}-y_{2}+2 y_{3}\\ y_{2}^{\prime }&=12 y_{1}-4 y_{2}+10 y_{3}\\ y_{3}^{\prime }&=-6 y_{1}+y_{2}-7 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.034 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}-y_{2}-4 y_{3}\\ y_{2}^{\prime }&=4 y_{1}-3 y_{2}-2 y_{3}\\ y_{3}^{\prime }&=y_{1}-y_{2}-y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.052 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-2 y_{1}+2 y_{2}-6 y_{3}\\ y_{2}^{\prime }&=2 y_{1}+6 y_{2}+2 y_{3}\\ y_{3}^{\prime }&=-2 y_{1}-2 y_{2}+2 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.987 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+2 y_{2}-2 y_{3}\\ y_{2}^{\prime }&=-2 y_{1}+7 y_{2}-2 y_{3}\\ y_{3}^{\prime }&=-10 y_{1}+10 y_{2}-5 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.882 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+y_{2}-y_{3}\\ y_{2}^{\prime }&=3 y_{1}+5 y_{2}+y_{3}\\ y_{3}^{\prime }&=-6 y_{1}+2 y_{2}+4 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.807 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+4 y_{2}\\ y_{2}^{\prime }&=-y_{1}+7 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{2}\\ y_{2}^{\prime }&=y_{1}-2 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-7 y_{1}+4 y_{2}\\ y_{2}^{\prime }&=-y_{1}-11 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.418 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=3 y_{1}+y_{2}\\ y_{2}^{\prime }&=-y_{1}+y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}+12 y_{2}\\ y_{2}^{\prime }&=-3 y_{1}-8 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.379 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-10 y_{1}+9 y_{2}\\ y_{2}^{\prime }&=-4 y_{1}+2 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-13 y_{1}+16 y_{2}\\ y_{2}^{\prime }&=-9 y_{1}+11 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{2}+y_{3}\\ y_{2}^{\prime }&=-4 y_{1}+6 y_{2}+y_{3}\\ y_{3}^{\prime }&=4 y_{2}+2 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.834 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=\frac {y_{1}}{3}+\frac {y_{2}}{3}-y_{3}\\ y_{2}^{\prime }&=-\frac {4 y_{1}}{3}-\frac {4 y_{2}}{3}+y_{3}\\ y_{3}^{\prime }&=-\frac {2 y_{1}}{3}+\frac {y_{2}}{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.841 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}+y_{2}-y_{3}\\ y_{2}^{\prime }&=-2 y_{1}+2 y_{3}\\ y_{3}^{\prime }&=-y_{1}+3 y_{2}-y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.818 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}-2 y_{2}-2 y_{3}\\ y_{2}^{\prime }&=-2 y_{1}+3 y_{2}-y_{3}\\ y_{3}^{\prime }&=2 y_{1}-y_{2}+3 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.975 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=6 y_{1}-5 y_{2}+3 y_{3}\\ y_{2}^{\prime }&=2 y_{1}-y_{2}+3 y_{3}\\ y_{3}^{\prime }&=2 y_{1}+y_{2}+y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.011 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-11 y_{1}+8 y_{2}\\ y_{2}^{\prime }&=-2 y_{1}-3 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=15 y_{1}-9 y_{2}\\ y_{2}^{\prime }&=16 y_{1}-9 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.481 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-3 y_{1}-4 y_{2}\\ y_{2}^{\prime }&=y_{1}-7 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-7 y_{1}+24 y_{2}\\ y_{2}^{\prime }&=-6 y_{1}+17 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.415 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-7 y_{1}+3 y_{2}\\ y_{2}^{\prime }&=-3 y_{1}-y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}+y_{2}\\ y_{2}^{\prime }&=y_{1}-y_{2}-2 y_{3}\\ y_{3}^{\prime }&=-y_{1}-y_{2}-y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.948 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-2 y_{1}+2 y_{2}+y_{3}\\ y_{2}^{\prime }&=-2 y_{1}+2 y_{2}+y_{3}\\ y_{3}^{\prime }&=-3 y_{1}+3 y_{2}+2 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-7 y_{1}-4 y_{2}+4 y_{3}\\ y_{2}^{\prime }&=y_{1}+y_{3}\\ y_{3}^{\prime }&=-9 y_{1}-5 y_{2}+6 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.666 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}-4 y_{2}-y_{3}\\ y_{2}^{\prime }&=3 y_{1}+6 y_{2}+y_{3}\\ y_{3}^{\prime }&=-3 y_{1}-2 y_{2}+3 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=4 y_{1}-8 y_{2}-4 y_{3}\\ y_{2}^{\prime }&=-3 y_{1}-y_{2}-4 y_{3}\\ y_{3}^{\prime }&=y_{1}-y_{2}+9 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.015 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-5 y_{1}-y_{2}+11 y_{3}\\ y_{2}^{\prime }&=-7 y_{1}+y_{2}+13 y_{3}\\ y_{3}^{\prime }&=-4 y_{1}+8 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=5 y_{1}-y_{2}+y_{3}\\ y_{2}^{\prime }&=-y_{1}+9 y_{2}-3 y_{3}\\ y_{3}^{\prime }&=-2 y_{1}+2 y_{2}+4 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.855 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+10 y_{2}-12 y_{3}\\ y_{2}^{\prime }&=2 y_{1}+2 y_{2}+3 y_{3}\\ y_{3}^{\prime }&=2 y_{1}-y_{2}+6 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-4 y_{3}\\ y_{2}^{\prime }&=2 y_{1}-y_{2}+y_{3}\\ y_{3}^{\prime }&=2 y_{1}+3 y_{2}+y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.726 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{2}-2 y_{3}\\ y_{2}^{\prime }&=-y_{1}+5 y_{2}-3 y_{3}\\ y_{3}^{\prime }&=y_{1}+y_{2}+y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-2 y_{1}-12 y_{2}+10 y_{3}\\ y_{2}^{\prime }&=2 y_{1}-24 y_{2}+11 y_{3}\\ y_{3}^{\prime }&=2 y_{1}-24 y_{2}+8 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.906 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}-12 y_{2}+8 y_{3}\\ y_{2}^{\prime }&=y_{1}-9 y_{2}+4 y_{3}\\ y_{3}^{\prime }&=y_{1}-6 y_{2}+y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.797 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-4 y_{1}-y_{3}\\ y_{2}^{\prime }&=-y_{1}-3 y_{2}-y_{3}\\ y_{3}^{\prime }&=y_{1}-2 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.727 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-3 y_{1}-3 y_{2}+4 y_{3}\\ y_{2}^{\prime }&=4 y_{1}+5 y_{2}-8 y_{3}\\ y_{3}^{\prime }&=2 y_{1}+3 y_{2}-5 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-3 y_{1}-y_{2}\\ y_{2}^{\prime }&=y_{1}-y_{2}\\ y_{3}^{\prime }&=-y_{1}-y_{2}-2 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.692 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-y_{1}+2 y_{2}\\ y_{2}^{\prime }&=-5 y_{1}+5 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.775 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-11 y_{1}+4 y_{2}\\ y_{2}^{\prime }&=-26 y_{1}+9 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=y_{1}+2 y_{2}\\ y_{2}^{\prime }&=-4 y_{1}+5 y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=5 y_{1}-6 y_{2}\\ y_{2}^{\prime }&=3 y_{1}-y_{2}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-3 y_{1}-3 y_{2}+y_{3}\\ y_{2}^{\prime }&=2 y_{2}+2 y_{3}\\ y_{3}^{\prime }&=5 y_{1}+y_{2}+y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
18.567 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-3 y_{1}+3 y_{2}+y_{3}\\ y_{2}^{\prime }&=y_{1}-5 y_{2}-3 y_{3}\\ y_{3}^{\prime }&=-3 y_{1}+7 y_{2}+3 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.616 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=2 y_{1}+y_{2}-y_{3}\\ y_{2}^{\prime }&=y_{2}+y_{3}\\ y_{3}^{\prime }&=y_{1}+y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.477 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y_{1}^{\prime }&=-3 y_{1}+y_{2}-3 y_{3}\\ y_{2}^{\prime }&=4 y_{1}-y_{2}+2 y_{3}\\ y_{3}^{\prime }&=4 y_{1}-2 y_{2}+3 y_{3}\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.310 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\sin \left (t \right ) y&=0\\ y \left (0\right )&={\frac {3}{2}}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+{\mathrm e}^{t^{2}} y&=0\\ y \left (1\right )&=2\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
44.259 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-2 t y&=t \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t y+y^{\prime }&=t\\ y \left (1\right )&=2\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=\frac {1}{t^{2}+1}\\ y \left (2\right )&=3\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.573 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \cos \left (t \right )+y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.062 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.938 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {2 t y}{t^{2}+1}+y^{\prime }&=\frac {1}{t^{2}+1} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.609 |
|