|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.179 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.175 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = x^{4}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.872 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.057 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (x +1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.642 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.385 |
|
|
\[
{}\left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.700 |
|
|
\[
{}\left (2 x -1\right )^{3} y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.642 |
|
|
\[
{}y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.496 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.963 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.113 |
|
|
\[
{}\left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.751 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 c +\frac {10}{x}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.622 |
|
|
\[
{}16 \left (x +1\right )^{4} y^{\prime \prime \prime \prime }+96 \left (x +1\right )^{3} y^{\prime \prime \prime }+104 \left (x +1\right )^{2} y^{\prime \prime }+8 \left (x +1\right ) y^{\prime }+y = x^{2}+4 x +3
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.055 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.628 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{m}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
37.673 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (\ln \left (x \right )+1\right )^{2}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.970 |
|
|
\[
{}x^{4} y^{\prime \prime \prime }+2 x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x y = 1
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.346 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
7.784 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
489.690 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+y = \frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
115.751 |
|
|
\[
{}x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✗ |
0.031 |
|
|
\[
{}x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
178.519 |
|
|
\[
{}x y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
155.470 |
|
|
\[
{}y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
275.191 |
|
|
\[
{}\sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
32.218 |
|
|
\[
{}y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime } = x y^{2}
\] |
[[_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]] |
✗ |
429.931 |
|
|
\[
{}x^{2} y y^{\prime \prime }+\left (-y+x y^{\prime }\right )^{2}-3 y^{2} = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
123.223 |
|