|
# |
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]] |
✓ |
0.872 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{-2 x} \cos \left (2 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.171 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime } = x^{2} \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.193 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = x^{2} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.602 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.921 |
|
|
\[
{}y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.037 |
|
|
\[
{}y^{\prime \prime }-y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.762 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{x}+\sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.177 |
|
|
\[
{}y^{\left (5\right )}+y^{\prime \prime \prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.135 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }-2 y = x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.453 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.634 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = x \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.140 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime } = x \cos \left (2 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.208 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.976 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = x^{2} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.976 |
|
|
\[
{}y^{\prime \prime }-y = x \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.808 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = x^{3} \sin \left (2 x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
4.111 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = x \,{\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.083 |
|
|
\[
{}y^{\prime \prime }-4 y = x \,{\mathrm e}^{2 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.836 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.257 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.435 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +16 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.423 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-16 y^{\prime } x +25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.128 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.618 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x -18 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.454 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y = \ln \left (x^{2}\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.477 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.585 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 1-x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.771 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y = \frac {1}{x}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.266 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 4 x +\sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.540 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.542 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +3 y = \left (x -1\right ) \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.991 |
|
|
\[
{}4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-y^{\prime } x +y = x +\ln \left (x \right )
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.329 |
|
|
\[
{}3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 y^{\prime } x +10 y = \frac {4}{x^{2}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.484 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 y^{\prime } x -6 y = \cos \left (\ln \left (x \right )\right )
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.636 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }-y^{\prime } x +4 y = \sin \left (\ln \left (x \right )\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.782 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x=\cos \left (t \right ) \\ y^{\prime }+y=4 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.375 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x=3 t^{2} \\ y^{\prime }+y={\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.365 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x=3 t \\ x^{\prime }+2 y^{\prime }+y=\cos \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.576 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+y=2 \sin \left (t \right ) \\ x^{\prime }+y^{\prime }=3 y-3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.553 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+3 x-y={\mathrm e}^{t} \\ 5 x-3 y^{\prime }=y+2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.568 |
|
|
\[
{}\left [\begin {array}{c} 5 y^{\prime }-3 x^{\prime }-5 y=5 t \\ 3 x^{\prime }-5 y^{\prime }-2 x=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.196 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=2 x+3 y \\ z^{\prime }=3 y-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.440 |
|
|
\[
{}y^{\prime \prime } = \cos \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.077 |
|
|
\[
{}y^{\prime \prime } = k^{2} y
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.235 |
|
|
\[
{}x^{\prime \prime }+k^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.802 |
|
|
\[
{}y^{3} y^{\prime \prime }+4 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.112 |
|
|
\[
{}x^{\prime \prime } = \frac {k^{2}}{x^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
71.539 |
|
|
\[
{}x y^{\prime \prime } = x^{2}+1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.931 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.009 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.401 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.914 |
|
|
\[
{}x y^{\prime \prime }+x = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.190 |
|
|
\[
{}x^{\prime \prime }+t x^{\prime } = t^{3}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.707 |
|
|
\[
{}x^{2} y^{\prime \prime } = y^{\prime } x +1
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.936 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.702 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
34.785 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.379 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime }
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.700 |
|
|
\[
{}y^{\prime \prime } = y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.657 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.779 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.596 |
|
|
\[
{}y^{\prime \prime }+2 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.369 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.414 |
|
|
\[
{}y y^{\prime \prime }+1 = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.148 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.306 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.707 |
|
|
\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.335 |
|
|
\[
{}y^{\prime \prime }+2 {y^{\prime }}^{2} = 2
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.894 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.488 |
|
|
\[
{}\left (1+y\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.520 |
|
|
\[
{}y^{\prime \prime } = \sec \left (x \right ) \tan \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
6.369 |
|
|
\[
{}2 y^{\prime \prime } = {\mathrm e}^{y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
18.624 |
|
|
\[
{}y^{\prime \prime } = y^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.714 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2} \cos \left (x \right )
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.536 |
|
|
\[
{}y y^{\prime \prime }-y^{2} y^{\prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.680 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.622 |
|
|
\[
{}y y^{\prime \prime } = y^{3}+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.416 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right )^{2} = y^{2} y^{\prime \prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
14.169 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.466 |
|
|
\[
{}2 y y^{\prime \prime } = y^{3}+2 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.381 |
|
|
\[
{}x^{\prime \prime }-k^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.303 |
|
|
\[
{}y y^{\prime \prime } = 2 {y^{\prime }}^{2}+y^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.694 |
|
|
\[
{}\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime } = {\mathrm e}^{x} y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.226 |
|
|
\[
{}4 y^{2} = {y^{\prime }}^{2} x^{2}
\] |
[_separable] |
✓ |
4.230 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
2.077 |
|
|
\[
{}1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.203 |
|
|
\[
{}x \left ({y^{\prime }}^{2}-1\right ) = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.326 |
|
|
\[
{}\left (1-y^{2}\right ) {y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.606 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x y-1\right ) y^{\prime } = y
\] |
[‘y=_G(x,y’)‘] |
✓ |
9.093 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+x y y^{\prime }-2 x^{2} = 0
\] |
[_separable] |
✓ |
6.661 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2} = x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.763 |
|
|
\[
{}{y^{\prime }}^{3}+\left (x +y-2 x y\right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right ) = 0
\] |
[_quadrature] |
✓ |
3.201 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (y^{2}-x^{3}-x y^{2}\right ) y^{\prime }-x y \left (x^{2}+y^{2}\right ) = 0
\] |
[_quadrature] |
✓ |
2.653 |
|
|
\[
{}y = y^{\prime } x \left (y^{\prime }+1\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.786 |
|
|
\[
{}y = x +3 \ln \left (y^{\prime }\right )
\] |
[_separable] |
✓ |
2.371 |
|
|
\[
{}y \left (1+{y^{\prime }}^{2}\right ) = 2
\] |
[_quadrature] |
✓ |
0.499 |
|
|
\[
{}y {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.899 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = 1
\] |
[_quadrature] |
✓ |
0.519 |
|
|
\[
{}x \left ({y^{\prime }}^{2}-1\right ) = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.351 |
|