|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime } = x^{2} \left (b x +a \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.140 |
|
|
\[
{}y^{\prime \prime \prime }-13 y^{\prime }+12 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.106 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = \cos \left (m x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.166 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.119 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.969 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.374 |
|
|
\[
{}y^{\prime \prime }+n^{2} y = x^{4} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.898 |
|
|
\[
{}y^{\prime \prime \prime \prime }-a^{4} y = x^{4}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.133 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x
\] |
[[_high_order, _missing_y]] |
✓ |
0.115 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = {\mathrm e}^{x} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.138 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
76.986 |
|
|
\[
{}y^{\prime \prime \prime }-7 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (x +1\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.137 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
47.534 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.124 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y = x^{2} {\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.139 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = x \,{\mathrm e}^{x}+{\mathrm e}^{x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime }-y = x \sin \left (x \right )+\left (x^{2}+1\right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
36.813 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = {\mathrm e}^{x} \cos \left (2 x \right )+\cos \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.548 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = {\mathrm e}^{x}+\cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.171 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+20 y = 20 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.339 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = {\mathrm e}^{3 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime }+y = {\mathrm e}^{2 x} \sin \left (x \right )+{\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
1.226 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 2 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.797 |
|
|
\[
{}x^{2} y^{\prime \prime }+y = 3 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.437 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.138 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.175 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y = x^{4}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.569 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.551 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -20 y = \left (x +1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.362 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y = x^{5}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.668 |
|
|
\[
{}\left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.674 |
|
|
\[
{}\left (2 x -1\right )^{3} y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.484 |
|
|
\[
{}y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.462 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.054 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 y^{\prime } x -8 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.126 |
|
|
\[
{}\left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.468 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.124 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 c +\frac {10}{x}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.815 |
|
|
\[
{}16 \left (x +1\right )^{4} y^{\prime \prime \prime \prime }+96 \left (x +1\right )^{3} y^{\prime \prime \prime }+104 \left (x +1\right )^{2} y^{\prime \prime }+8 \left (x +1\right ) y^{\prime }+y = x^{2}+4 x +3
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.082 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{m}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.104 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{m}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.714 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \left (1+\ln \left (x \right )\right )^{2}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.777 |
|
|
\[
{}x^{4} y^{\prime \prime \prime }+2 x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x y = 1
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.242 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {1}{\left (1-x \right )^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.190 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
18.912 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +y = \frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.546 |
|
|
\[
{}x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.289 |
|
|
\[
{}x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.777 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.141 |
|
|
\[
{}y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.914 |
|
|
\[
{}\sqrt {x}\, y^{\prime \prime }+2 y^{\prime } x +3 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.787 |
|
|
\[
{}y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime } = x y^{2}
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
4.650 |
|
|
\[
{}x^{2} y y^{\prime \prime }+\left (-y+y^{\prime } x \right )^{2}-3 y^{2} = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.697 |
|
|
\[
{}y^{\prime \prime \prime } = x \,{\mathrm e}^{x}
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.109 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+1 = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.216 |
|
|
\[
{}y^{\prime \prime } = x^{2} \sin \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.361 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.712 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{\sqrt {a y}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.018 |
|
|
\[
{}y^{\prime \prime }+\frac {a^{2}}{y^{2}} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
71.008 |
|
|
\[
{}y^{\prime \prime }-\frac {a^{2}}{y^{2}} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
71.787 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-4 x y^{\prime \prime }+6 y^{\prime } = 4
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.204 |
|
|
\[
{}y^{\prime \prime } = \sqrt {{y^{\prime }}^{2}+1}
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.390 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.723 |
|
|
\[
{}2 x y^{\prime \prime \prime } y^{\prime \prime } = {y^{\prime \prime }}^{2}-a^{2}
\] |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.781 |
|
|
\[
{}y^{\prime \prime }-a {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.352 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.304 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.062 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.441 |
|
|
\[
{}y^{\prime \prime \prime \prime }+a^{2} y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\left (5\right )}-m^{2} y^{\prime \prime \prime } = {\mathrm e}^{a x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.125 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+a^{2} y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.475 |
|
|
\[
{}a^{2} y^{\prime \prime } y^{\prime } = x
\] |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.401 |
|
|
\[
{}a y^{\prime \prime } = \sqrt {{y^{\prime }}^{2}+1}
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.074 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.838 |
|
|
\[
{}y^{\prime \prime \prime } y^{\prime \prime } = 2
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.441 |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime \prime }+4 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.894 |
|
|
\[
{}x^{4} y^{\prime \prime }+y^{\prime } x +y = \frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.100 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.388 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.592 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.867 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.718 |
|
|
\[
{}\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} \left (x +y\right )+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
145.465 |
|
|
\[
{}y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )} = \frac {x^{2}}{a \left (a^{2}-x^{2}\right )}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.646 |
|
|
\[
{}\left (x^{3}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✗ |
3.162 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y = 2 x
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.385 |
|
|
\[
{}y^{\prime \prime \prime \prime }-a^{2} y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}{y^{\prime }}^{2}-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
42.102 |
|
|
\[
{}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 y^{\prime } x +4 y = \frac {2}{x^{3}}
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.821 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x = 2
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.338 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y^{\prime } \cos \left (x \right )+2 \sin \left (x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.372 |
|
|
\[
{}x y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.253 |
|
|
\[
{}y^{\prime \prime } = \frac {a}{x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.943 |
|
|
\[
{}y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.477 |
|
|
\[
{}y^{\prime \prime \prime } = \sin \left (x \right )^{2}
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.146 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.036 |
|
|
\[
{}y^{\prime \prime \prime }+\cos \left (x \right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.753 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime } = 2 y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.790 |
|
|
\[
{}a y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.199 |
|
|
\[
{}y^{3} y^{\prime \prime } = a
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.017 |
|