|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = x \,{\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.674 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.240 |
|
|
\[
{}m x^{\prime \prime } = f \left (x\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.205 |
|
|
\[
{}m x^{\prime \prime } = f \left (x^{\prime }\right )
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.609 |
|
|
\[
{}y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = x
\] |
[[_high_order, _missing_y]] |
✓ |
0.131 |
|
|
\[
{}x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x = \cos \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.037 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 2 \cos \left (\ln \left (x +1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.561 |
|
|
\[
{}x^{3} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.334 |
|
|
\[
{}x^{\prime \prime \prime \prime }+x = t^{3}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.131 |
|
|
\[
{}{y^{\prime \prime }}^{3}+y^{\prime \prime }+1 = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.520 |
|
|
\[
{}x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.490 |
|
|
\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}-y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.268 |
|
|
\[
{}y^{\left (6\right )}-y = {\mathrm e}^{2 x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.163 |
|
|
\[
{}y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime } = x +{\mathrm e}^{x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.158 |
|
|
\[
{}6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0
\] |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] |
✓ |
0.319 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.596 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (3 x \right ) \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.368 |
|
|
\[
{}y^{\prime \prime } = 2 y^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.349 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.273 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.396 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x+y={\mathrm e}^{t} \\ y^{\prime }-x-3 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.885 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=z \\ z^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.844 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=\frac {y^{2}}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.049 |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{x +y} \left (x^{2}+1\right )
\] |
[_separable] |
✓ |
1.539 |
|
|
\[
{}x^{2} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
1.808 |
|
|
\[
{}y^{\prime } = \sin \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.415 |
|
|
\[
{}x \left ({\mathrm e}^{y}+4\right ) = {\mathrm e}^{x +y} y^{\prime }
\] |
[_separable] |
✓ |
2.281 |
|
|
\[
{}y^{\prime } = \cos \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.435 |
|
|
\[
{}x y^{\prime }+y = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.273 |
|
|
\[
{}y^{\prime } = t \ln \left (y^{2 t}\right )+t^{2}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.846 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{y^{2}-x}
\] |
[_separable] |
✓ |
1.263 |
|
|
\[
{}y^{\prime } = \ln \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.700 |
|
|
\[
{}x \left (1+y\right )^{2} = \left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime }
\] |
[_separable] |
✓ |
2.386 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.881 |
|
|
\[
{}y^{\prime \prime \prime }+x y = \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.048 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
5.481 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime } = 2 x^{2}+3
\] |
[[_high_order, _missing_y]] |
✓ |
0.155 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
0.046 |
|
|
\[
{}y^{\prime \prime \prime }+x y = \cosh \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.047 |
|
|
\[
{}y^{\prime } \cos \left (x \right )+y \,{\mathrm e}^{x^{2}} = \sinh \left (x \right )
\] |
[_linear] |
✓ |
39.327 |
|
|
\[
{}y^{\prime \prime \prime }+x y = \cosh \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.048 |
|
|
\[
{}y y^{\prime } = 1
\] |
[_quadrature] |
✓ |
1.300 |
|
|
\[
{}\sinh \left (x \right ) {y^{\prime }}^{2}+3 y = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.551 |
|
|
\[
{}5 y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
1.199 |
|
|
\[
{}{y^{\prime }}^{2} \sqrt {y} = \sin \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.325 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.555 |
|
|
\[
{}y^{\prime \prime \prime } = 1
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.095 |
|
|
\[
{}x^{2} y^{\prime \prime }-y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.495 |
|
|
\[
{}y^{\prime \prime } = y+x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.020 |
|
|
\[
{}y^{\prime \prime \prime }+x y^{\prime \prime }-y^{2} = \sin \left (x \right )
\] |
[NONE] |
✗ |
0.052 |
|
|
\[
{}{y^{\prime }}^{2}+x y {y^{\prime }}^{2} = \ln \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
6.103 |
|
|
\[
{}\sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
0.051 |
|
|
\[
{}\sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = x y
\] |
[NONE] |
✗ |
0.133 |
|
|
\[
{}y y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.481 |
|
|
\[
{}{y^{\prime \prime \prime }}^{2}+\sqrt {y} = \sin \left (x \right )
\] |
[NONE] |
✗ |
0.023 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.114 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.114 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.831 |
|
|
\[
{}3 y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}\left (x -3\right ) y^{\prime \prime }+y \ln \left (x \right ) = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.208 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cot \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.148 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.066 |
|
|
\[
{}x y^{\prime \prime }+2 x^{2} y^{\prime }+y \sin \left (x \right ) = \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.546 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.013 |
|
|
\[
{}y^{\prime \prime }-\left (x -1\right ) y^{\prime }+x^{2} y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.775 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.281 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.625 |
|
|
\[
{}y^{\prime \prime }+\frac {k x}{y^{4}} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.127 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.030 |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.854 |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y^{\prime }+4 x y = 2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.591 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = -2 x +1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.905 |
|
|
\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.701 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.606 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.529 |
|
|
\[
{}\ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.643 |
|
|
\[
{}x y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.468 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = \cos \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.231 |
|
|
\[
{}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }-\csc \left (x \right )^{2} y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.352 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x} = 1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.162 |
|
|
\[
{}x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1 = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
1.128 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1+y}+\frac {y y^{\prime }-x {y^{\prime }}^{2}+y^{\prime }}{\left (1+y\right )^{2}} = x \sin \left (x \right )
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.451 |
|
|
\[
{}\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime \prime }-x {y^{\prime }}^{2} \sin \left (y\right )+2 \left (\cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime } = y \sin \left (x \right )
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
79.734 |
|
|
\[
{}y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+y \cos \left (x \right )\right ) y^{\prime } = \cos \left (x \right )
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.661 |
|
|
\[
{}\left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.546 |
|
|
\[
{}\left (\cos \left (y\right )-y \sin \left (y\right )\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right ) = \sin \left (x \right )
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.974 |
|
|
\[
{}y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.922 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.451 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x +1}-\frac {\left (x +2\right ) y}{x^{2} \left (x +1\right )} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.285 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.351 |
|
|
\[
{}\frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (3 x +1\right ) y^{\prime }}{x}+\frac {y}{x} = 3 x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.433 |
|
|
\[
{}\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
9.389 |
|
|
\[
{}y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}} = \frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.327 |
|
|
\[
{}y^{\prime \prime }+\left (2 x +5\right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.754 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.294 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.311 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.234 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.289 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.247 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+37 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.340 |
|