| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.090 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-8 y^{\prime }+8 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.093 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-6 y^{\prime }+2 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }-4 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+10 y^{\prime }-15 y&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.083 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+11 y^{\prime }-40 y&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.086 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-12 y^{\prime }+16 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.096 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.086 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }-6 y^{\prime \prime }+8 y^{\prime }-8 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=3 \cos \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (2 x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-2 x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=x \,{\mathrm e}^{-x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{x} \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=x +{\mathrm e}^{2 x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-9 y&={\mathrm e}^{3 x}+\sin \left (3 x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.002 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-6 y&=x^{3} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y^{\prime \prime }+3 y&=x \,{\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=x \sin \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-4 y^{\prime \prime }&=x^{2}+8 \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{x} \sin \left (3 x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-12 y&=x +{\mathrm e}^{2 x} \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y&={\mathrm e}^{4 x} \sin \left (x \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+4 y&=x^{3} {\mathrm e}^{2 x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{2 x} \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\sin \left (k x \right ) \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 n y^{\prime }+n^{2} y&=5 \cos \left (6 x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.110 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+5 y&=2 x -{\mathrm e}^{-4 x}+\sin \left (2 x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.160 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+2 y^{\prime \prime }&=\left (2 x^{2}+x \right ) {\mathrm e}^{-2 x}+5 \cos \left (3 x \right ) \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=8 \sin \left (x \right )^{2} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+4 y&=5 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x}\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=12 \cos \left (x \right )^{2}\\ y \left (\frac {\pi }{2}\right )&=0\\ y^{\prime }\left (\frac {\pi }{2}\right )&=\frac {\pi }{2}\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.975 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=x \,{\mathrm e}^{-x}\\ y \left (0\right )&={\frac {1}{9}}\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&={\mathrm e}^{x} \sin \left (x \right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.904 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+y^{\prime }&=8 \sin \left (2 x \right )+{\mathrm e}^{-x}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.450 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=3 x \sin \left (x \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+5 y^{\prime }-3 y&=\sin \left (x \right )-8 x\\ y \left (0\right )&={\frac {1}{2}}\\ y^{\prime }\left (0\right )&={\frac {1}{2}}\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 8 y^{\prime \prime }-y&=x \,{\mathrm e}^{-\frac {x}{2}}\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sec \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{2 x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=4 \sin \left (2 x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.538 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=2 x -2 \sin \left (2 x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=3 x +5 \,{\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&={\mathrm e}^{x}+\sin \left (4 x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.988 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }&=\cos \left (2 x \right ) \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.192 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime }&={\mathrm e}^{3 x} \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\tan \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a^{2} y&=\sec \left (a x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.327 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x} \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.181 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \end {array} \]
|
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{2 x}+\sin \left (x \right ) \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.510 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=\sin \left ({\mathrm e}^{-x}\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\sec \left (x \right ) \tan \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y&={\mathrm e}^{-x} \sin \left (2 x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\csc \left (x \right ) \sec \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\csc \left (2 x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\tan \left (\frac {x}{3}\right )^{2} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.430 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime }&=\tan \left (x \right ) \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }-4 y^{\prime }+y&={\mathrm e}^{\frac {x}{2}} \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.517 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+P \left (x \right ) y&=Q \left (x \right ) \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.972 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.184 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&=x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=2 \,{\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y&=3 \,{\mathrm e}^{-4 x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.567 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{-2 x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y&=\sin \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{3 x}}{2}-\frac {{\mathrm e}^{-3 x}}{2} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }-2 y&=\sin \left (2 x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.472 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y&={\mathrm e}^{x} \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.145 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y&=\sin \left (x \right )-{\mathrm e}^{4 x} \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.732 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y&=4 \,{\mathrm e}^{x}+3 \cos \left (2 x \right ) \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.696 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&={\mathrm e}^{3 x} \left (1+\sin \left (2 x \right )\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.970 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y&=\sin \left (k x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+5 y&=\frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{-x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=x \,{\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.501 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y&=x^{2} {\mathrm e}^{-x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=x^{2}-8 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y&=x^{2} \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.141 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime }&=x^{2} {\mathrm e}^{-x} \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \end {array} \]
|
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.193 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{x} \left (\sin \left (x \right )-x^{2}\right ) \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-4 y^{\prime \prime }&={\mathrm e}^{2 x} \left (x -3\right ) \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=\sin \left (3 x \right )+x \,{\mathrm e}^{x} \end {array} \]
|
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.653 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x^{2} {\mathrm e}^{2 x} \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+2 y^{\prime }&=x^{2}+\cos \left (x \right ) \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }+2 y&=\sin \left (2 x \right ) \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.238 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=x^{3}-\frac {\cos \left (2 x \right )}{2} \end {array} \]
|
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }&={\mathrm e}^{-2 x} \cos \left (x \right ) \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.565 |
|