|
# |
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]] |
✓ |
0.625 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{-2 x} \cos \left (2 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime } = x^{2} \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.178 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = x^{2} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.674 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.808 |
|
|
\[
{}y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.823 |
|
|
\[
{}y^{\prime \prime }-y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.661 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{x}+\sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.142 |
|
|
\[
{}y^{\left (5\right )}+y^{\prime \prime \prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.113 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }-2 y = x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.178 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.382 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = x \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.127 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime } = x \cos \left (2 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.260 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.751 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = x^{2} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.750 |
|
|
\[
{}y^{\prime \prime }-y = x \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.732 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = x^{3} \sin \left (2 x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
4.370 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = x \,{\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.326 |
|
|
\[
{}y^{\prime \prime }-4 y = x \,{\mathrm e}^{2 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.681 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.241 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.201 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+16 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.313 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.895 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.333 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }-18 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.188 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = \ln \left (x^{2}\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.298 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.329 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 1-x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.595 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {1}{x}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.302 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 4 x +\sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.384 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
40.673 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+3 y = \left (-1+x \right ) \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
71.122 |
|
|
\[
{}4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-x y^{\prime }+y = x +\ln \left (x \right )
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.355 |
|
|
\[
{}3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 x y^{\prime }+10 y = \frac {4}{x^{2}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.444 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 x y^{\prime }-6 y = \cos \left (\ln \left (x \right )\right )
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.463 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }-x y^{\prime }+4 y = \sin \left (\ln \left (x \right )\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.865 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x=\cos \left (t \right ) \\ y^{\prime }+y=4 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.406 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x=3 t^{2} \\ y^{\prime }+y={\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.376 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x=3 t \\ x^{\prime }+2 y^{\prime }+y=\cos \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.661 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+y=2 \sin \left (t \right ) \\ x^{\prime }+y^{\prime }=3 y-3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.604 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+3 x-y={\mathrm e}^{t} \\ 5 x-3 y^{\prime }=y+2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.630 |
|
|
\[
{}\left [\begin {array}{c} 5 y^{\prime }-3 x^{\prime }-5 y=5 t \\ 3 x^{\prime }-5 y^{\prime }-2 x=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.178 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=2 x+3 y \\ z^{\prime }=3 y-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.395 |
|
|
\[
{}y^{\prime \prime } = \cos \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.924 |
|
|
\[
{}y^{\prime \prime } = k^{2} y
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.625 |
|
|
\[
{}x^{\prime \prime }+k^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.646 |
|
|
\[
{}y^{3} y^{\prime \prime }+4 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.228 |
|
|
\[
{}x^{\prime \prime } = \frac {k^{2}}{x^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
67.075 |
|
|
\[
{}x y^{\prime \prime } = x^{2}+1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.789 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.809 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.349 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.255 |
|
|
\[
{}x y^{\prime \prime }+x = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.123 |
|
|
\[
{}x^{\prime \prime }+t x^{\prime } = t^{3}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.511 |
|
|
\[
{}x^{2} y^{\prime \prime } = x y^{\prime }+1
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.764 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.401 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
34.526 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.003 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime }
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.938 |
|
|
\[
{}y^{\prime \prime } = y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.355 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.746 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.994 |
|
|
\[
{}y^{\prime \prime }+2 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.447 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.104 |
|
|
\[
{}y y^{\prime \prime }+1 = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.140 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.016 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.589 |
|
|
\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.348 |
|
|
\[
{}y^{\prime \prime }+2 {y^{\prime }}^{2} = 2
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.680 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x]] |
✓ |
6.078 |
|
|
\[
{}\left (y+1\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.737 |
|
|
\[
{}y^{\prime \prime } = \sec \left (x \right ) \tan \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
6.365 |
|
|
\[
{}2 y^{\prime \prime } = {\mathrm e}^{y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.303 |
|
|
\[
{}y^{\prime \prime } = y^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.645 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2} \cos \left (x \right )
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
1.328 |
|
|
\[
{}y y^{\prime \prime }-y^{2} y^{\prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.892 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.938 |
|
|
\[
{}y y^{\prime \prime } = y^{3}+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✗ |
868.724 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right )^{2} = y^{2} y^{\prime \prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
9.185 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.803 |
|
|
\[
{}2 y y^{\prime \prime } = y^{3}+2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✗ |
417.451 |
|
|
\[
{}x^{\prime \prime }-k^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.620 |
|
|
\[
{}y y^{\prime \prime } = 2 {y^{\prime }}^{2}+y^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
7.239 |
|
|
\[
{}\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime } = {\mathrm e}^{x} y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.023 |
|
|
\[
{}4 y^{2} = {y^{\prime }}^{2} x^{2}
\] |
[_separable] |
✓ |
2.787 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.481 |
|
|
\[
{}1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.549 |
|
|
\[
{}x \left ({y^{\prime }}^{2}-1\right ) = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.030 |
|
|
\[
{}\left (1-y^{2}\right ) {y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
30.075 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x y-1\right ) y^{\prime } = y
\] |
[‘y=_G(x,y’)‘] |
✓ |
11.784 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+x y y^{\prime }-2 x^{2} = 0
\] |
[_separable] |
✓ |
1.485 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2} = x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
13.066 |
|
|
\[
{}{y^{\prime }}^{3}+\left (x +y-2 x y\right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right ) = 0
\] |
[_quadrature] |
✓ |
1.111 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (y^{2}-x^{3}-x y^{2}\right ) y^{\prime }-x y \left (x^{2}+y^{2}\right ) = 0
\] |
[_quadrature] |
✓ |
0.988 |
|
|
\[
{}y = y^{\prime } x \left (y^{\prime }+1\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.840 |
|
|
\[
{}y = x +3 \ln \left (y^{\prime }\right )
\] |
[_separable] |
✓ |
2.654 |
|
|
\[
{}y \left (1+{y^{\prime }}^{2}\right ) = 2
\] |
[_quadrature] |
✓ |
0.454 |
|
|
\[
{}y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.687 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = 1
\] |
[_quadrature] |
✓ |
0.726 |
|
|
\[
{}x \left ({y^{\prime }}^{2}-1\right ) = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
0.997 |
|