|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+9 y = \ln \left (2 \sin \left (\frac {x}{2}\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
118.069 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.352 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.643 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.972 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.088 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = x^{3}+3 x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.295 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 4 \cos \left (\ln \left (x +1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.296 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+\left (1-\frac {m^{2}}{x^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.068 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
1.633 |
|
|
\[
{}y^{\prime \prime }+\frac {2 p y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
1.122 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.313 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.036 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {y \left (-8+\sqrt {x}+x \right )}{4 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.293 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=z \\ z^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.800 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=y+z \\ z^{\prime }=y+z+x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.379 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=\frac {y^{2}}{z} \\ z^{\prime }=\frac {y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.052 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=1-\frac {1}{z} \\ z^{\prime }=\frac {1}{y-x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.052 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=-z \\ z^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.408 |
|
|
\[
{}y^{\prime \prime } = x +y^{2}
\] |
[NONE] |
✗ |
0.088 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_Emden, _modified]] |
✗ |
0.437 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=\frac {z^{2}}{y} \\ z^{\prime }=\frac {y^{2}}{z} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.051 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=\frac {y^{2}}{z} \\ z^{\prime }=\frac {z^{2}}{y} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.051 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z-x \\ y^{\prime }=x-y+z \\ z^{\prime }=x+y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.364 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x+y=t^{2} \\ y^{\prime }+y+z=2 t \\ z^{\prime }+z=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.539 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x+y=7 \,{\mathrm e}^{t}-27 \\ -2 x+y^{\prime }+3 y=-3 \,{\mathrm e}^{t}+12 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.861 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime \prime }+z^{\prime }-2 z={\mathrm e}^{2 x} \\ z^{\prime }+2 y^{\prime }-3 y=0 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.050 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x+{\mathrm e}^{t}+{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.502 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+\frac {2 z}{x^{2}}=1 \\ z^{\prime }+y=x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.049 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime } t -x-3 y=t \\ t y^{\prime }-x+y=0 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.051 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime } t +6 x-y-3 z=0 \\ t y^{\prime }+23 x-6 y-9 z=0 \\ t z^{\prime }+x+y-2 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.055 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x+y={\mathrm e}^{t} \\ y^{\prime }-x+3 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.512 |
|
|
\[
{}y^{\prime } = 2 x
\] |
[_quadrature] |
✓ |
0.263 |
|
|
\[
{}x y^{\prime } = 2 y
\] |
[_separable] |
✓ |
1.646 |
|
|
\[
{}y^{\prime } y = {\mathrm e}^{2 x}
\] |
[_separable] |
✓ |
1.398 |
|
|
\[
{}y^{\prime } = k y
\] |
[_quadrature] |
✓ |
0.711 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.494 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.387 |
|
|
\[
{}x y^{\prime }+y = y^{\prime } \sqrt {1-x^{2} y^{2}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
3.991 |
|
|
\[
{}x y^{\prime } = y+x^{2}+y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.408 |
|
|
\[
{}y^{\prime } = \frac {x y}{y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.855 |
|
|
\[
{}2 x y y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.721 |
|
|
\[
{}x y^{\prime }+y = x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.964 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x y-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.529 |
|
|
\[
{}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.636 |
|
|
\[
{}1+y^{2}+y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
4.045 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x}-x
\] |
[_quadrature] |
✓ |
0.313 |
|
|
\[
{}x y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.313 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.306 |
|
|
\[
{}y^{\prime } = \arcsin \left (x \right )
\] |
[_quadrature] |
✓ |
0.288 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.349 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.356 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.493 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \arctan \left (x \right )
\] |
[_quadrature] |
✓ |
0.405 |
|
|
\[
{}x y y^{\prime } = y-1
\] |
[_separable] |
✓ |
1.381 |
|
|
\[
{}x^{5} y^{\prime }+y^{5} = 0
\] |
[_separable] |
✓ |
4.968 |
|
|
\[
{}x y^{\prime } = \left (-2 x^{2}+1\right ) \tan \left (y\right )
\] |
[_separable] |
✓ |
2.017 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
1.156 |
|
|
\[
{}y^{\prime } \sin \left (y\right ) = x^{2}
\] |
[_separable] |
✓ |
1.348 |
|
|
\[
{}y^{\prime } \sin \left (x \right ) = 1
\] |
[_quadrature] |
✓ |
0.444 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.334 |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.398 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+1+y^{2} = 0
\] |
[_separable] |
✓ |
1.884 |
|
|
\[
{}y \ln \left (y\right )-x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.705 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.545 |
|
|
\[
{}y^{\prime } = 2 \sin \left (x \right ) \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.609 |
|
|
\[
{}y^{\prime } = \ln \left (x \right )
\] |
[_quadrature] |
✓ |
0.513 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.477 |
|
|
\[
{}x \left (x^{2}-4\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.652 |
|
|
\[
{}\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime } = 2 x^{2}+x
\] |
[_quadrature] |
✓ |
1.089 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-2 y+3 x}
\] |
[_separable] |
✓ |
3.673 |
|
|
\[
{}x y^{\prime } = 2 x^{2}+1
\] |
[_quadrature] |
✓ |
0.532 |
|
|
\[
{}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.265 |
|
|
\[
{}3 \cos \left (3 x \right ) \cos \left (2 y\right )-2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
4.459 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.687 |
|
|
\[
{}x y y^{\prime } = \left (x +1\right ) \left (y+1\right )
\] |
[_separable] |
✓ |
1.440 |
|
|
\[
{}y^{\prime } = 2 x y+1
\] |
[_linear] |
✓ |
0.920 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.408 |
|
|
\[
{}2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}v^{\prime } = g -\frac {k v^{2}}{m}
\] |
[_quadrature] |
✓ |
0.836 |
|
|
\[
{}x^{2}-2 y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
70.940 |
|
|
\[
{}x^{2} y^{\prime }-3 x y-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.400 |
|
|
\[
{}x^{2} y^{\prime } = 3 \left (y^{2}+x^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
14.593 |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.558 |
|
|
\[
{}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
26.610 |
|
|
\[
{}x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.704 |
|
|
\[
{}x y^{\prime } = 2 x +3 y
\] |
[_linear] |
✓ |
1.951 |
|
|
\[
{}x y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.308 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.178 |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.734 |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.545 |
|
|
\[
{}y^{\prime } = \sin \left (x +1-y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
8.314 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x -y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.860 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x +y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.297 |
|
|
\[
{}2 x -2 y+\left (y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.927 |
|
|
\[
{}y^{\prime } = \frac {y-1+x}{x +4 y+2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.073 |
|
|
\[
{}2 x +3 y-1-4 \left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.674 |
|
|
\[
{}y^{\prime } = \frac {1-x y^{2}}{2 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.750 |
|
|
\[
{}y^{\prime } = \frac {2+3 x y^{2}}{4 x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.424 |
|
|
\[
{}y^{\prime } = \frac {y-x y^{2}}{x +x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.639 |
|
|
\[
{}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.490 |
|