|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} \left (x +y\right )+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
148.979 |
|
|
\[
{}y^{\prime \prime \prime } = x \,{\mathrm e}^{x}
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.132 |
|
|
\[
{}y^{\prime \prime } = x^{2} \sin \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.729 |
|
|
\[
{}y^{\prime \prime } = \sec \left (x \right )^{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.891 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.235 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.881 |
|
|
\[
{}y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.617 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.957 |
|
|
\[
{}y^{\prime }-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }}
\] |
[[_2nd_order, _missing_x]] |
✗ |
19.602 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.033 |
|
|
\[
{}y^{\prime \prime \prime \prime }-a^{2} y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}x^{4} y^{\prime \prime } = \left (y-y^{\prime } x \right )^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.144 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } = x^{2} y^{\prime }-y^{2}
\] |
[NONE] |
✗ |
0.186 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.099 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime } = 2 y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.791 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -y = x \left (-x^{2}+1\right )^{{3}/{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.697 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y = \left (x +1\right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.957 |
|
|
\[
{}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\left (1-\cot \left (x \right )\right ) y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
2.053 |
|
|
\[
{}\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
9.685 |
|
|
\[
{}y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y = x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.636 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.019 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.784 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.332 |
|
|
\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+y = 0
\] |
[_Lienard] |
✓ |
3.477 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.574 |
|
|
\[
{}y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y = {\mathrm e}^{6 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.072 |
|
|
\[
{}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+\frac {\csc \left (x \right )^{2} y}{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.282 |
|
|
\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.037 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{3} \sin \left (x^{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.977 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 y \cos \left (x \right )^{3} = 2 \cos \left (x \right )^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.591 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 4 \cos \left (\ln \left (x +1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.551 |
|
|
\[
{}x y^{\prime \prime }+\left (x -1\right ) y^{\prime }-y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.436 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+6 x +2\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.740 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.553 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.671 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.112 |
|
|
\[
{}y^{\prime \prime }+\left (1-\cot \left (x \right )\right ) y^{\prime }-y \cot \left (x \right ) = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
2.241 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{2 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.143 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-7 x+y=0 \\ y^{\prime }-2 x-5 y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.572 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x+y={\mathrm e}^{t} \\ y^{\prime }-x+3 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.585 |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }+9 y^{\prime }+11 x+31 y={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+8 x+24 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.617 |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }=t -2 x \\ t y^{\prime }=t x+t y+2 x-t \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.059 |
|