|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime }+y = 3+{\mathrm e}^{-x}+5 \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.151 |
|
|
\[
{}y^{\prime \prime \prime }-y = \left ({\mathrm e}^{x}+1\right )^{2}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.145 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{\frac {5 x}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.158 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.105 |
|
|
\[
{}y^{\prime \prime \prime }+8 y = x^{4}+2 x +1
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.115 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.145 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \cos \left (a x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.532 |
|
|
\[
{}y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.499 |
|
|
\[
{}y^{\prime \prime \prime }+y = \sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.352 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y = x \,{\mathrm e}^{2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.136 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.493 |
|
|
\[
{}y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.694 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.749 |
|
|
\[
{}y^{\prime \prime }-y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.695 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x}+x^{2}+x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.126 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (3 x \right )+{\mathrm e}^{x}+x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.756 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x +{\mathrm e}^{m x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.319 |
|
|
\[
{}y^{\prime \prime }-a^{2} y = {\mathrm e}^{a x}+{\mathrm e}^{n x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.118 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-6 y^{\prime }+8 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.097 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime } = x^{2} \left (b x +a \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime }-13 y^{\prime }+12 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.095 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = \cos \left (m x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.164 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.944 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.005 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.254 |
|
|
\[
{}y^{\prime \prime }+n^{2} y = x^{4} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.188 |
|
|
\[
{}y^{\prime \prime \prime \prime }-a^{4} y = x^{4}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.123 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x
\] |
[[_high_order, _missing_y]] |
✓ |
0.099 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = {\mathrm e}^{x} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.128 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
77.670 |
|
|
\[
{}y^{\prime \prime \prime }-7 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (x +1\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
45.351 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.113 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y = x^{2} {\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.132 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = x \,{\mathrm e}^{x}+{\mathrm e}^{x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.140 |
|
|
\[
{}y^{\prime \prime }-y = x \sin \left (x \right )+\left (x^{2}+1\right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
36.268 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = {\mathrm e}^{x} \cos \left (2 x \right )+\cos \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.528 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = {\mathrm e}^{x}+\cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.169 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+20 y = 20 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.152 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = {\mathrm e}^{3 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.100 |
|
|
\[
{}y^{\prime \prime \prime }+y = {\mathrm e}^{2 x} \sin \left (x \right )+{\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
1.422 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 2 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.694 |
|
|
\[
{}x^{2} y^{\prime \prime }+y = 3 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.257 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.122 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.133 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = x^{4}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.441 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.396 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (x +1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.191 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.609 |
|
|
\[
{}\left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.768 |
|
|
\[
{}\left (2 x -1\right )^{3} y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.503 |
|
|
\[
{}y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.458 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.944 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.111 |
|
|
\[
{}\left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.289 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.114 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 c +\frac {10}{x}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.725 |
|
|
\[
{}16 \left (x +1\right )^{4} y^{\prime \prime \prime \prime }+96 \left (x +1\right )^{3} y^{\prime \prime \prime }+104 \left (x +1\right )^{2} y^{\prime \prime }+8 \left (x +1\right ) y^{\prime }+y = x^{2}+4 x +3
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.055 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.213 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{m}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.517 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (1+\ln \left (x \right )\right )^{2}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.879 |
|
|
\[
{}x^{4} y^{\prime \prime \prime }+2 x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x y = 1
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.296 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.071 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
53.849 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+y = \frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.215 |
|
|
\[
{}x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.391 |
|
|
\[
{}x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.725 |
|
|
\[
{}x y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.156 |
|
|
\[
{}y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.777 |
|
|
\[
{}\sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.822 |
|
|
\[
{}y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime } = x y^{2}
\] |
[[_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]] |
✗ |
5.555 |
|
|
\[
{}x^{2} y y^{\prime \prime }+\left (-y+x y^{\prime }\right )^{2}-3 y^{2} = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.980 |
|
|
\[
{}y^{\prime \prime \prime } = x \,{\mathrm e}^{x}
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.097 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+1 = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.213 |
|
|
\[
{}y^{\prime \prime } = x^{2} \sin \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.335 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.707 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{\sqrt {a y}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
30.605 |
|
|
\[
{}y^{\prime \prime }+\frac {a^{2}}{y^{2}} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
66.271 |
|
|
\[
{}y^{\prime \prime }-\frac {a^{2}}{y^{2}} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
66.344 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-4 x y^{\prime \prime }+6 y^{\prime } = 4
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.187 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.209 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.845 |
|
|
\[
{}2 x y^{\prime \prime \prime } y^{\prime \prime } = {y^{\prime \prime }}^{2}-a^{2}
\] |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.865 |
|
|
\[
{}y^{\prime \prime }-a {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.462 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
3.319 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.162 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
5.652 |
|
|
\[
{}y^{\prime \prime \prime \prime }+a^{2} y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}y^{\left (5\right )}-m^{2} y^{\prime \prime \prime } = {\mathrm e}^{a x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.118 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+a^{2} y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.532 |
|
|
\[
{}a^{2} y^{\prime \prime } y^{\prime } = x
\] |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.822 |
|
|
\[
{}a y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.549 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.734 |
|
|
\[
{}y^{\prime \prime \prime } y^{\prime \prime } = 2
\] |
[[_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]] |
✓ |
0.497 |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime \prime }+4 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.715 |
|
|
\[
{}x^{4} y^{\prime \prime }+x y^{\prime }+y = \frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.083 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.373 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.396 |
|