|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }+4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
19.648 |
|
|
\[
{}x y^{\prime \prime \prime }+x y^{\prime } = 4
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.793 |
|
|
\[
{}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.460 |
|
|
\[
{}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.729 |
|
|
\[
{}\sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.816 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right ) = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.357 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.168 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.148 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.063 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.339 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.747 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.092 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.928 |
|
|
\[
{}y^{\prime \prime }-4 y = 31
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.275 |
|
|
\[
{}y^{\prime \prime }+9 y = 27 x +18
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.242 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = -3 x -\frac {3}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.710 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.064 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+6 y^{\prime }-4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.081 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.098 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.099 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.093 |
|
|
\[
{}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.095 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.100 |
|
|
\[
{}y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.116 |
|
|
\[
{}y^{\prime \prime }+\alpha y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
38.749 |
|
|
\[
{}y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.106 |
|
|
\[
{}y^{\prime \prime \prime \prime }+\left (-3-i\right ) y^{\prime \prime \prime }+\left (4+3 i\right ) y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.090 |
|
|
\[
{}y^{\prime }-i y = 0
\] |
[_quadrature] |
✓ |
1.190 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.188 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 24 x^{2}-6 x +14+32 \cos \left (2 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.594 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3+\cos \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.181 |
|
|
\[
{}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 6 x -20-120 x^{2} {\mathrm e}^{x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.181 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y = 36 \,{\mathrm e}^{2 x} \sin \left (3 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.528 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.267 |
|
|
\[
{}y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y = {\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.266 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.154 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 2 \,{\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.146 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 x +4
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.150 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.259 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.219 |
|
|
\[
{}y^{\prime }+2 y = 4
\] |
[_quadrature] |
✓ |
0.282 |
|
|
\[
{}y^{\prime \prime }-9 y = 2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.230 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.229 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{x}-3 x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.229 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{x}-3 x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.317 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.571 |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.370 |
|
|
\[
{}y^{\prime \prime }-9 y = x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.332 |
|
|
\[
{}y^{\prime \prime }+9 y = x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.394 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.639 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = -x^{2}+1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.344 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x +\cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.444 |
|
|
\[
{}y^{\prime }-2 y = 6
\] |
[_quadrature] |
✓ |
0.465 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.464 |
|
|
\[
{}y^{\prime \prime }+9 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.325 |
|
|
\[
{}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.380 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.216 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.272 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.359 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.431 |
|
|
\[
{}y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.774 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.605 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (-1+x \right )^{2} & 1\le x \end {array}\right .
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.881 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.032 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.753 |
|
|
\[
{}y^{\prime \prime }-4 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.996 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.645 |
|
|
\[
{}y^{\prime }+3 y = \delta \left (-2+x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.586 |
|
|
\[
{}y^{\prime }-3 y = \delta \left (-1+x \right )+2 \operatorname {Heaviside}\left (-2+x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.783 |
|
|
\[
{}y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.822 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \delta \left (-1+x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.642 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \delta \left (x -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.359 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (x \right ) \delta \left (x -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.612 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \delta \left (x -\pi \right ) f \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.616 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.469 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-2 y_{2} \\ y_{2}^{\prime }=y_{1}+3 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.548 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2}+x -1 \\ y_{2}^{\prime }=3 y_{1}+2 y_{2}-5 x -2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.597 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {2 y_{1}}{x}-\frac {y_{2}}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}} \\ y_{2}^{\prime }=2 y_{1}+1-6 x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.039 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.040 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}-2 y_{2} \\ y_{2}^{\prime }=y_{2}-y_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.829 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.043 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.043 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\ y_{2}^{\prime }=\frac {y_{1}}{\left (-2+x \right )^{2}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.041 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\ y_{2}^{\prime }=\frac {y_{1}}{\left (-2+x \right )^{2}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.042 |
|
|
\(\left [\begin {array}{cc} -2 & -4 \\ 1 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.115 |
|
|
\(\left [\begin {array}{cc} -3 & -1 \\ 2 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.169 |
|
|
\(\left [\begin {array}{ccc} 1 & 0 & 1 \\ 0 & 1 & -1 \\ -2 & 0 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.306 |
|
|
\(\left [\begin {array}{ccc} 3 & 1 & -1 \\ 1 & 3 & -1 \\ 3 & 3 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.225 |
|
|
\(\left [\begin {array}{ccc} 7 & -1 & 6 \\ -10 & 4 & -12 \\ -2 & 1 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.279 |
|
|
\(\left [\begin {array}{cccc} 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.263 |
|
|
\(\left [\begin {array}{cccc} 1 & 3 & 5 & 7 \\ 2 & 6 & 10 & 14 \\ 3 & 9 & 15 & 21 \\ 6 & 18 & 30 & 42 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.280 |
|
|
\(\left [\begin {array}{ccccc} 1 & 3 & 5 & 2 & 4 \\ 5 & 2 & 4 & 1 & 3 \\ 4 & 1 & 3 & 5 & 2 \\ 3 & 5 & 2 & 4 & 1 \\ 2 & 4 & 1 & 3 & 5 \end {array}\right ]\) |
Eigenvectors |
✓ |
5.074 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2}+5 \,{\mathrm e}^{x} \\ y_{2}^{\prime }=y_{1}+4 y_{2}-2 \,{\mathrm e}^{-x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.369 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}-2 y_{1}+\sin \left (2 x \right ) \\ y_{2}^{\prime }=-3 y_{1}+y_{2}-2 \cos \left (3 x \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
3.274 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{2} \\ y_{2}^{\prime }=3 y_{1} \\ y_{3}^{\prime }=2 y_{3}-y_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.701 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 x y_{1}-x^{2} y_{2}+4 x \\ y_{2}^{\prime }={\mathrm e}^{x} y_{1}+3 \,{\mathrm e}^{-x} y_{2}-\cos \left (3 x \right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.042 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.456 |
|