|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y = y^{\prime } x +y^{\prime }-{y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.487 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } = x y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.199 |
|
|
\[
{}y-2 y^{\prime } x -y {y^{\prime }}^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.808 |
|
|
\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
1.266 |
|
|
\[
{}y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x} = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.181 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y = \frac {1}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.706 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.263 |
|
|
\[
{}v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.669 |
|
|
\[
{}y^{\prime \prime }-2 y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.597 |
|
|
\[
{}y^{\prime \prime }-{y^{\prime }}^{2}-y {y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.375 |
|
|
\[
{}\left ({y^{\prime }}^{2}+1\right )^{{3}/{2}} = r y^{\prime \prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
8.391 |
|
|
\[
{}y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5} = 0
\] |
[[_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.172 |
|
|
\[
{}\left (1+y^{2}\right ) y^{\prime \prime }-2 y {y^{\prime }}^{2}-2 \left (1+y^{2}\right ) y^{\prime } = y^{2} \left (1+y^{2}\right )
\] |
[[_2nd_order, _missing_x]] |
✗ |
3.274 |
|
|
\[
{}y^{2} y^{\prime \prime \prime }-\left (3 y y^{\prime }+2 x y^{2}\right ) y^{\prime \prime }+\left (2 {y^{\prime }}^{2}+2 x y y^{\prime }+3 x^{2} y^{2}\right ) y^{\prime }+x^{3} y^{3} = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.117 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.227 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.892 |
|
|
\[
{}x^{3} v^{\prime \prime \prime }+2 x^{2} v^{\prime \prime }+v = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.175 |
|
|
\[
{}v^{\prime \prime }+\frac {2 x v^{\prime }}{x^{2}+1}+\frac {v}{\left (x^{2}+1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.090 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = -x^{2}+1
\] |
[_linear] |
✓ |
1.227 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \csc \left (x \right )^{2}
\] |
[_linear] |
✓ |
1.589 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.221 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x^{2} y = x^{3}-x^{2} \arctan \left (x \right )
\] |
[_linear] |
✗ |
33.027 |
|
|
\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
1.265 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}-1\right ) y = x^{3}
\] |
[_linear] |
✓ |
1.470 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
2.170 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3}
\] |
[_linear] |
✓ |
1.077 |
|
|
\[
{}y^{\prime }+\sin \left (x \right ) y = y^{2} \sin \left (x \right )
\] |
[_separable] |
✓ |
2.618 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2}
\] |
[_separable] |
✓ |
2.094 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right )
\] |
[_Bernoulli] |
✓ |
4.729 |
|
|
\[
{}3 y^{2} y^{\prime }+y^{3} = x -1
\] |
[_rational, _Bernoulli] |
✓ |
1.798 |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = y^{4} \sec \left (x \right )
\] |
[_Bernoulli] |
✓ |
2.846 |
|
|
\[
{}y \sqrt {x^{2}-1}+x \sqrt {y^{2}-1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
2.067 |
|
|
\[
{}\left ({\mathrm e}^{y}+1\right ) \cos \left (x \right )+{\mathrm e}^{y} \sin \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.184 |
|
|
\[
{}\sqrt {2 a y-y^{2}}\, \csc \left (x \right )+y \tan \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
6.494 |
|
|
\[
{}y \left (3+y\right ) y^{\prime } = x \left (2 y+3\right )
\] |
[_separable] |
✓ |
2.020 |
|
|
\[
{}x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.648 |
|
|
\[
{}x^{3}+4 x y+y^{2}+\left (2 x^{2}+2 x y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.552 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.481 |
|
|
\[
{}x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y} = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.169 |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+x^{2}+2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
74.668 |
|
|
\[
{}5 x y y^{\prime }-x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
31.355 |
|
|
\[
{}\left (x^{2}+3 x y-y^{2}\right ) y^{\prime }-3 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.878 |
|
|
\[
{}\left (x^{2}+2 x y\right ) y^{\prime }-3 x^{2}+2 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.431 |
|
|
\[
{}5 x y y^{\prime }-4 x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
9.597 |
|
|
\[
{}\left (x^{2}-2 x y\right ) y^{\prime }+x^{2}-3 x y+2 y^{2} = 0
\] |
[_linear] |
✓ |
1.520 |
|
|
\[
{}3 x^{2} y^{\prime }+2 x^{2}-3 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.474 |
|
|
\[
{}\left (3 x +2 y-7\right ) y^{\prime } = 2 x -3 y+6
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.717 |
|
|
\[
{}\left (6 x -5 y+4\right ) y^{\prime } = 2 x -y+1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
53.108 |
|
|
\[
{}\left (5 x -2 y+7\right ) y^{\prime } = x -3 y+2
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.271 |
|
|
\[
{}\left (x -3 y+4\right ) y^{\prime } = 5 x -7 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.022 |
|
|
\[
{}\left (x -3 y+4\right ) y^{\prime } = 2 x -6 y+7
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.888 |
|
|
\[
{}\left (5 x -2 y+7\right ) y^{\prime } = 10 x -4 y+6
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.832 |
|
|
\[
{}\left (2 x -2 y+5\right ) y^{\prime } = x -y+3
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.790 |
|
|
\[
{}\left (6 x -4 y+1\right ) y^{\prime } = 3 x -2 y+1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.865 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.065 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.255 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.065 |
|
|
\[
{}2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-5 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.259 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime } = x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.120 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+2 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.923 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.727 |
|
|
\[
{}y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime } = x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.112 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.326 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.343 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.187 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.053 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.836 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = x^{4}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.116 |
|
|
\[
{}e y^{\prime \prime } = \frac {P \left (\frac {L}{2}-x \right )}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.076 |
|
|
\[
{}e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.040 |
|
|
\[
{}e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.153 |
|
|
\[
{}e y^{\prime \prime } = -P \left (L -x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.006 |
|
|
\[
{}e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.220 |
|
|
\[
{}e y^{\prime \prime } = P \left (-y+a \right )
\] |
[[_2nd_order, _missing_x]] |
✓ |
49.230 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 y^{\prime } x = \ln \left (x \right )^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.269 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x -8 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.309 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = x^{3}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.232 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y = \ln \left (x \right )
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.261 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.122 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } = 2 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.030 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.704 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.263 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.237 |
|
|
\[
{}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\csc \left (x \right )^{2} y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.246 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.329 |
|
|
\[
{}\left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y = \sin \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.628 |
|
|
\[
{}\left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y = x^{3}
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.204 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime } = -\frac {1}{x^{2}}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.209 |
|
|
\[
{}y^{\prime \prime } = \cos \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.025 |
|
|
\[
{}x^{2} y^{\prime \prime } = \ln \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.707 |
|
|
\[
{}y^{\prime \prime } = -a^{2} y
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.714 |
|