|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.217 |
|
|
\[
{}{y^{\prime }}^{3}-\left (2 x +y^{2}\right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2} = 0
\] |
[_quadrature] |
✓ |
1.250 |
|
|
\[
{}2 x y^{\prime }-y+\ln \left (y^{\prime }\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
2.204 |
|
|
\[
{}4 x {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
12.386 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
0.959 |
|
|
\[
{}y^{\prime }+2 x y = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.710 |
|
|
\[
{}y = -x y^{\prime }+x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.725 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.441 |
|
|
\[
{}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.963 |
|
|
\[
{}a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.345 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
0.968 |
|
|
\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
10.501 |
|
|
\[
{}\left (-y+x y^{\prime }\right )^{2} = 1+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.624 |
|
|
\[
{}4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1 = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
8.592 |
|
|
\[
{}4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.337 |
|
|
\[
{}{\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
295.114 |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.388 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
147.738 |
|
|
\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
107.721 |
|
|
\[
{}a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.369 |
|
|
\[
{}\left (x -y^{\prime }-y\right )^{2} = x^{2} \left (2 x y-x^{2} y^{\prime }\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
79.651 |
|
|
\[
{}y^{2} \left (1+{y^{\prime }}^{2}\right ) = a^{2}
\] |
[_quadrature] |
✓ |
0.569 |
|
|
\[
{}y y^{\prime } = \left (x -b \right ) {y^{\prime }}^{2}+a
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.509 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.840 |
|
|
\[
{}3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.862 |
|
|
\[
{}y = {y^{\prime }}^{2} \left (x +1\right )
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.799 |
|
|
\[
{}\left (-y+x y^{\prime }\right ) \left (x +y y^{\prime }\right ) = a^{2} y^{\prime }
\] |
[_rational] |
✓ |
122.762 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right ) = y^{2}
\] |
[_separable] |
✓ |
1.233 |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.639 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 \left (x y+2 y^{\prime }\right ) y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
0.770 |
|
|
\[
{}y = x y^{\prime }+\frac {y {y^{\prime }}^{2}}{x^{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.889 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} = y^{2} x^{2}+x^{4}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
9.678 |
|
|
\[
{}y = x y^{\prime }+\frac {1}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.429 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
0.961 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 \left (x y-2\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
0.572 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (-1+x \right )^{2} = 0
\] |
[_quadrature] |
✓ |
0.596 |
|
|
\[
{}8 \left (1+y^{\prime }\right )^{3} = 27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
31.210 |
|
|
\[
{}4 {y^{\prime }}^{2} = 9 x
\] |
[_quadrature] |
✓ |
0.322 |
|
|
\[
{}y \left (3-4 y\right )^{2} {y^{\prime }}^{2} = 4-4 y
\] |
[_quadrature] |
✓ |
0.522 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.853 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.581 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.064 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.051 |
|
|
\[
{}4 y^{\prime \prime \prime }-3 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.052 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.058 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.051 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.055 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{-x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.098 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{{\mathrm e}^{x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.143 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}-x^{2} {\mathrm e}^{-x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.143 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.710 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.995 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.103 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.829 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.100 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.878 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.883 |
|
|
\[
{}y^{\prime \prime }+4 y = x^{2}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.477 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{2 x}-\sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.744 |
|
|
\[
{}y^{\prime \prime }+y = 2 \,{\mathrm e}^{x}+x^{3}-x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.131 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{2 x}-\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.630 |
|
|
\[
{}y^{\prime \prime \prime }-y = x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime } = 3 x^{2}+\sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.175 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = {\mathrm e}^{x}+4
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.129 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{2 x}+1
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.196 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.779 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x y^{\prime }-y = \ln \left (x \right ) x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.295 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 x +\frac {10}{x}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.774 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.752 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }+6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
17.638 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \cos \left (x \right )-{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.809 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = {\mathrm e}^{x} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.124 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 x^{3}-x \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.355 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = x^{2}-3 \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.117 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (1+\ln \left (x \right )\right )^{2}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.851 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = x^{2}-x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.102 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.960 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.577 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y = {\mathrm e}^{3 x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.123 |
|
|
\[
{}y^{\prime \prime }+y = x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.505 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {1}{x}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.304 |
|
|
\[
{}y^{\prime \prime \prime }-y = x \,{\mathrm e}^{x}+\cos \left (x \right )^{2}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
1.094 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.568 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = x^{2}-x -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.866 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.684 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.525 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 \sin \left (x \right ) y = {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
41.664 |
|
|
\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-\left (a^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.088 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.707 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y = 2 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.786 |
|
|
\[
{}y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+{\mathrm e}^{2 x} y = {\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.801 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.367 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.265 |
|
|
\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.590 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-8 x^{3} y = 4 x^{3} {\mathrm e}^{-x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.398 |
|
|
\[
{}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y = 0
\] |
[_Laguerre] |
✓ |
0.839 |
|
|
\[
{}\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.034 |
|