|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime } = {\mathrm e}^{-2 x} \cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.655 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{-2 x} \cos \left (2 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.197 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime } = x^{2} \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.212 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = x^{2} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.103 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.286 |
|
|
\[
{}y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.885 |
|
|
\[
{}y^{\prime \prime }-y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.752 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{x}+\sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.178 |
|
|
\[
{}y^{\left (5\right )}+y^{\prime \prime \prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.156 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }-2 y = x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.311 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.720 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = x \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.178 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime } = x \cos \left (2 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.244 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.997 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = x^{2} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.958 |
|
|
\[
{}y^{\prime \prime }-y = x \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.858 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = x^{3} \sin \left (2 x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
4.053 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = x \,{\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.797 |
|
|
\[
{}y^{\prime \prime }-4 y = x \,{\mathrm e}^{2 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.799 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.038 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.770 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+16 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.657 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.510 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.991 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }-18 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.963 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = \ln \left (x^{2}\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.898 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.937 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 1-x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.116 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {1}{x}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.300 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 4 x +\sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.195 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.180 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+3 y = \left (x -1\right ) \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.588 |
|
|
\[
{}4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-x y^{\prime }+y = x +\ln \left (x \right )
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.431 |
|
|
\[
{}3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 x y^{\prime }+10 y = \frac {4}{x^{2}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.560 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 x y^{\prime }-6 y = \cos \left (\ln \left (x \right )\right )
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.870 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }-x y^{\prime }+4 y = \sin \left (\ln \left (x \right )\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.983 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x=\cos \left (t \right ) \\ y^{\prime }+y=4 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.463 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x=3 t^{2} \\ y^{\prime }+y={\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.425 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x=3 t \\ x^{\prime }+2 y^{\prime }+y=\cos \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.741 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+y=2 \sin \left (t \right ) \\ x^{\prime }+y^{\prime }=3 y-3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.634 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+3 x-y={\mathrm e}^{t} \\ 5 x-3 y^{\prime }=y+2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.678 |
|
|
\[
{}\left [\begin {array}{c} 5 y^{\prime }-3 x^{\prime }-5 y=5 t \\ 3 x^{\prime }-5 y^{\prime }-2 x=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.226 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=2 x+3 y \\ z^{\prime }=3 y-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.465 |
|
|
\[
{}y^{\prime \prime } = \cos \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.713 |
|
|
\[
{}y^{\prime \prime } = k^{2} y
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.977 |
|
|
\[
{}x^{\prime \prime }+k^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.023 |
|
|
\[
{}y^{3} y^{\prime \prime }+4 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.394 |
|
|
\[
{}x^{\prime \prime } = \frac {k^{2}}{x^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
73.090 |
|
|
\[
{}x y^{\prime \prime } = x^{2}+1
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.084 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.201 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.698 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.734 |
|
|
\[
{}x y^{\prime \prime }+x = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.398 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } t = t^{3}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.891 |
|
|
\[
{}x^{2} y^{\prime \prime } = x y^{\prime }+1
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.084 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.434 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
34.938 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.444 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime }
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.586 |
|
|
\[
{}y^{\prime \prime } = y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.731 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.857 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.633 |
|
|
\[
{}y^{\prime \prime }+2 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.218 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.476 |
|
|
\[
{}y y^{\prime \prime }+1 = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.403 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.212 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.820 |
|
|
\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.374 |
|
|
\[
{}y^{\prime \prime }+2 {y^{\prime }}^{2} = 2
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.337 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.771 |
|
|
\[
{}\left (y+1\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.513 |
|
|
\[
{}y^{\prime \prime } = \sec \left (x \right ) \tan \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
3.271 |
|
|
\[
{}2 y^{\prime \prime } = {\mathrm e}^{y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
20.460 |
|
|
\[
{}y^{\prime \prime } = y^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.816 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2} \cos \left (x \right )
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.605 |
|
|
\[
{}y y^{\prime \prime }-y^{2} y^{\prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.734 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.685 |
|
|
\[
{}y y^{\prime \prime } = y^{3}+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.776 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right )^{2} = y^{2} y^{\prime \prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
15.543 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.527 |
|
|
\[
{}2 y y^{\prime \prime } = y^{3}+2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.925 |
|
|
\[
{}x^{\prime \prime }-k^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.737 |
|
|
\[
{}y y^{\prime \prime } = 2 {y^{\prime }}^{2}+y^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.572 |
|
|
\[
{}\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime } = {\mathrm e}^{x} y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.222 |
|
|
\[
{}4 y^{2} = {y^{\prime }}^{2} x^{2}
\] |
[_separable] |
✓ |
3.004 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
1.489 |
|
|
\[
{}1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.102 |
|
|
\[
{}x \left (-1+{y^{\prime }}^{2}\right ) = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.386 |
|
|
\[
{}\left (1-y^{2}\right ) {y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.595 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x y-1\right ) y^{\prime } = y
\] |
[_rational] |
✓ |
8.203 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+x y y^{\prime }-2 x^{2} = 0
\] |
[_separable] |
✓ |
5.392 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2} = x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.800 |
|
|
\[
{}{y^{\prime }}^{3}+\left (x +y-2 x y\right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right ) = 0
\] |
[_quadrature] |
✓ |
2.240 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (y^{2}-x^{3}-x y^{2}\right ) y^{\prime }-x y \left (y^{2}+x^{2}\right ) = 0
\] |
[_quadrature] |
✓ |
2.152 |
|
|
\[
{}y = y^{\prime } x \left (y^{\prime }+1\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.803 |
|
|
\[
{}y = x +3 \ln \left (y^{\prime }\right )
\] |
[_separable] |
✓ |
2.042 |
|
|
\[
{}y \left (1+{y^{\prime }}^{2}\right ) = 2
\] |
[_quadrature] |
✓ |
0.484 |
|
|
\[
{}y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.787 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = 1
\] |
[_quadrature] |
✓ |
0.566 |
|
|
\[
{}x \left (-1+{y^{\prime }}^{2}\right ) = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.360 |
|