|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.669 |
|
|
\[
{}y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x} = x -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.743 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime \prime }-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }-2 x y = x^{4}+12
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.066 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.065 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.168 |
|
|
\[
{}y^{\prime \prime }+\frac {y}{x^{2} \ln \left (x \right )} = {\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.279 |
|
|
\[
{}y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.073 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.071 |
|
|
\[
{}y^{\prime \prime } \sin \left (x \right )^{2}+\sin \left (x \right ) \cos \left (x \right ) y^{\prime } = y
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.914 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.105 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.096 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.411 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{x}+{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.321 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.126 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = \left (x +1\right ) {\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.151 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.030 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
32.225 |
|
|
\[
{}y^{\prime \prime }-y = \frac {{\mathrm e}^{x}-{\mathrm e}^{-x}}{{\mathrm e}^{x}+{\mathrm e}^{-x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.890 |
|
|
\[
{}y^{\prime \prime }-2 y = 4 x^{2} {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.514 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.877 |
|
|
\[
{}y^{\prime \prime }+9 y = \ln \left (2 \sin \left (\frac {x}{2}\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
114.840 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.238 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.506 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = x \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.989 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.087 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = x^{3}+3 x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.270 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 4 \cos \left (\ln \left (x +1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.019 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+\left (1-\frac {m^{2}}{x^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.993 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
1.470 |
|
|
\[
{}y^{\prime \prime }+\frac {2 p y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
1.046 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.238 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.822 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {y \left (-8+\sqrt {x}+x \right )}{4 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.211 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=z \\ z^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.804 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=y+z \\ z^{\prime }=y+z+x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.365 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=\frac {y^{2}}{z} \\ z^{\prime }=\frac {y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.055 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=1-\frac {1}{z} \\ z^{\prime }=\frac {1}{y-x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.054 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=-z \\ z^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.475 |
|
|
\[
{}y^{\prime \prime } = x +y^{2}
\] |
[NONE] |
✗ |
0.133 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_Emden, _modified]] |
✗ |
1.285 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=\frac {z^{2}}{y} \\ z^{\prime }=\frac {y^{2}}{z} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.056 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=\frac {y^{2}}{z} \\ z^{\prime }=\frac {z^{2}}{y} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.057 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z-x \\ y^{\prime }=x-y+z \\ z^{\prime }=x+y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.345 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x+y=t^{2} \\ y^{\prime }+y+z=2 t \\ z^{\prime }+z=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.516 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x+y=7 \,{\mathrm e}^{t}-27 \\ -2 x+y^{\prime }+3 y=-3 \,{\mathrm e}^{t}+12 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.786 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime \prime }+z^{\prime }-2 z={\mathrm e}^{2 x} \\ z^{\prime }+2 y^{\prime }-3 y=0 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.055 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x+{\mathrm e}^{t}+{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+\frac {2 z}{x^{2}}=1 \\ z^{\prime }+y=x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.055 |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }-x-3 y=t \\ t y^{\prime }-x+y=0 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.060 |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }+6 x-y-3 z=0 \\ t y^{\prime }+23 x-6 y-9 z=0 \\ t z^{\prime }+x+y-2 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.066 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x+y={\mathrm e}^{t} \\ y^{\prime }-x+3 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.487 |
|
|
\[
{}y^{\prime } = 2 x
\] |
[_quadrature] |
✓ |
0.436 |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
2.129 |
|
|
\[
{}y y^{\prime } = {\mathrm e}^{2 x}
\] |
[_separable] |
✓ |
1.664 |
|
|
\[
{}y^{\prime } = k y
\] |
[_quadrature] |
✓ |
0.668 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.276 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.341 |
|
|
\[
{}y^{\prime } x +y = y^{\prime } \sqrt {1-x^{2} y^{2}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
3.987 |
|
|
\[
{}y^{\prime } x = y+x^{2}+y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.581 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.254 |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.674 |
|
|
\[
{}y^{\prime } x +y = x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.862 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x y-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
37.282 |
|
|
\[
{}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.723 |
|
|
\[
{}1+y^{2}+y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
4.176 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x}-x
\] |
[_quadrature] |
✓ |
0.500 |
|
|
\[
{}y^{\prime } x = 1
\] |
[_quadrature] |
✓ |
0.462 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.492 |
|
|
\[
{}y^{\prime } = \arcsin \left (x \right )
\] |
[_quadrature] |
✓ |
0.372 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.524 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.538 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.663 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \arctan \left (x \right )
\] |
[_quadrature] |
✓ |
0.582 |
|
|
\[
{}x y y^{\prime } = -1+y
\] |
[_separable] |
✓ |
1.600 |
|
|
\[
{}x^{5} y^{\prime }+y^{5} = 0
\] |
[_separable] |
✓ |
5.382 |
|
|
\[
{}y^{\prime } x = \left (-2 x^{2}+1\right ) \tan \left (y\right )
\] |
[_separable] |
✓ |
2.011 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
1.578 |
|
|
\[
{}y^{\prime } \sin \left (y\right ) = x^{2}
\] |
[_separable] |
✓ |
1.447 |
|
|
\[
{}y^{\prime } \sin \left (x \right ) = 1
\] |
[_quadrature] |
✓ |
0.611 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.755 |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.806 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+1+y^{2} = 0
\] |
[_separable] |
✓ |
2.079 |
|
|
\[
{}y \ln \left (y\right )-y^{\prime } x = 0
\] |
[_separable] |
✓ |
1.789 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.691 |
|
|
\[
{}y^{\prime } = 2 \sin \left (x \right ) \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.776 |
|
|
\[
{}y^{\prime } = \ln \left (x \right )
\] |
[_quadrature] |
✓ |
0.414 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.665 |
|
|
\[
{}x \left (x^{2}-4\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.796 |
|
|
\[
{}\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime } = 2 x^{2}+x
\] |
[_quadrature] |
✓ |
1.234 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x -2 y}
\] |
[_separable] |
✓ |
4.006 |
|
|
\[
{}y^{\prime } x = 2 x^{2}+1
\] |
[_quadrature] |
✓ |
0.771 |
|
|
\[
{}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.430 |
|
|
\[
{}3 \cos \left (3 x \right ) \cos \left (2 y\right )-2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
4.445 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.839 |
|
|
\[
{}x y y^{\prime } = \left (x +1\right ) \left (1+y\right )
\] |
[_separable] |
✓ |
1.442 |
|
|
\[
{}y^{\prime } = 2 x y+1
\] |
[_linear] |
✓ |
1.056 |
|