|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\sin \left (x \right ) u^{\prime \prime }+2 \cos \left (x \right ) u^{\prime }+\sin \left (x \right ) u = 0
\] |
[_Lienard] |
✓ |
3.503 |
|
|
\[
{}3 {y^{\prime \prime }}^{2}-y^{\prime } y^{\prime \prime \prime }-y^{\prime \prime } {y^{\prime }}^{2} = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.507 |
|
|
\[
{}y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1} = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.679 |
|
|
\[
{}x^{2} y y^{\prime \prime } = x^{2} {y^{\prime }}^{2}-y^{2}
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.169 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 4 \,{\mathrm e}^{t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.133 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 \sin \left (t \right )-5 \cos \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.345 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = g \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.499 |
|
|
\[
{}y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{t} = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.230 |
|
|
\[
{}x x^{\prime \prime }-{x^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.251 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-4 y = f \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.637 |
|
|
\[
{}u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.970 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 50 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.039 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 50 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.042 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.406 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \sin \left (3 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.164 |
|
|
\[
{}y^{\prime \prime }+4 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.891 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.190 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.919 |
|
|
\[
{}y+\sqrt {y^{2}+x^{2}}-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.620 |
|
|
\[
{}{y^{\prime }}^{2} = a^{2}-y^{2}
\] |
[_quadrature] |
✓ |
0.666 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.637 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.885 |
|
|
\[
{}y \left (x^{2} y^{2}+1\right )+\left (x^{2} y^{2}-1\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.889 |
|
|
\[
{}2 x^{3} y^{2}-y+\left (2 y^{3} x^{2}-x \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.519 |
|
|
\[
{}\frac {1}{y}+\sec \left (\frac {y}{x}\right )-\frac {x y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
16.897 |
|
|
\[
{}\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right ) = 0
\] |
[_Bernoulli] |
✓ |
2.695 |
|
|
\[
{}u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.744 |
|
|
\[
{}\left (\phi ^{\prime }-\frac {\phi ^{2}}{2}\right ) \sin \left (\theta \right )^{2}-\phi \sin \left (\theta \right ) \cos \left (\theta \right ) = \frac {\cos \left (2 \theta \right )}{2}+1
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
4.588 |
|
|
\[
{}a y^{\prime \prime } y^{\prime \prime \prime } = \sqrt {1+{y^{\prime \prime }}^{2}}
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
2.363 |
|
|
\[
{}a^{2} y^{\prime \prime \prime \prime } = y^{\prime \prime }
\] |
[[_high_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.600 |
|
|
\[
{}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.688 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.299 |
|
|
\[
{}\left (-x^{2}+1\right ) z^{\prime \prime }+\left (1-3 x \right ) z^{\prime }+k z = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.911 |
|
|
\[
{}\left (-x^{2}+1\right ) \eta ^{\prime \prime }-\left (x +1\right ) \eta ^{\prime }+\left (k +1\right ) \eta = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.890 |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.536 |
|
|
\[
{}x^{2}-y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
6.514 |
|
|
\[
{}-y+x y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.379 |
|
|
\[
{}-y+x y^{\prime } = x \sqrt {x^{2}-y^{2}}\, y^{\prime }
\] |
[‘y=_G(x,y’)‘] |
✗ |
4.372 |
|
|
\[
{}x +y^{\prime } y+y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.654 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}-y^{2} y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.415 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }=2 x_{1}-9 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.502 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{2} \\ x_{2}^{\prime }=5 x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.333 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+3 x_{2} \\ x_{2}^{\prime }=-3 x_{1}+5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.413 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}+2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.494 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.321 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }=x_{1}-2 x_{2}+3 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.503 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=16 x_{1}-5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.499 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=3 x_{1}-4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.454 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }=2 x_{1}-9 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.444 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+3 x_{2} \\ x_{2}^{\prime }=-3 x_{1}+5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.441 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }=2 x_{1}-9 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.510 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.480 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-8 \\ x_{2}^{\prime }=x_{1}+x_{2}+3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.431 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-8 \\ x_{2}^{\prime }=x_{1}+x_{2}+3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.611 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x}+\sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.378 |
|
|
\[
{}y^{\prime \prime } = x +2
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.265 |
|
|
\[
{}y^{\prime \prime \prime } = x^{2}
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.107 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
1.375 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \sin \left (x \right ) \cos \left (x \right )
\] |
[_linear] |
✓ |
1.665 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.934 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.983 |
|
|
\[
{}y^{\prime \prime }+k^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.642 |
|
|
\[
{}y^{\prime }+5 y = 2
\] |
[_quadrature] |
✓ |
1.040 |
|
|
\[
{}y^{\prime \prime } = 3 x +1
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.238 |
|
|
\[
{}y^{\prime } = k y
\] |
[_quadrature] |
✓ |
0.704 |
|
|
\[
{}y^{\prime }-2 y = 1
\] |
[_quadrature] |
✓ |
0.923 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.008 |
|
|
\[
{}y^{\prime }-2 y = x^{2}+x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.047 |
|
|
\[
{}3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.096 |
|
|
\[
{}y^{\prime }+3 y = {\mathrm e}^{i x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.858 |
|
|
\[
{}y^{\prime }+i y = x
\] |
[[_linear, ‘class A‘]] |
✓ |
0.981 |
|
|
\[
{}L y^{\prime }+R y = E
\] |
[_quadrature] |
✓ |
0.760 |
|
|
\[
{}L y^{\prime }+R y = E \sin \left (\omega x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.512 |
|
|
\[
{}L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.145 |
|
|
\[
{}y^{\prime }+a y = b \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.203 |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
1.098 |
|
|
\[
{}x y^{\prime }+y = 3 x^{3}-1
\] |
[_linear] |
✓ |
0.994 |
|
|
\[
{}y^{\prime }+y \,{\mathrm e}^{x} = 3 \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
1.235 |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = {\mathrm e}^{\sin \left (x \right )}
\] |
[_linear] |
✓ |
1.579 |
|
|
\[
{}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.187 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = {\mathrm e}^{-\sin \left (x \right )}
\] |
[_linear] |
✓ |
1.713 |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 1
\] |
[_linear] |
✓ |
1.208 |
|
|
\[
{}y^{\prime }+2 y = b \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.166 |
|
|
\[
{}y^{\prime } = y+1
\] |
[_quadrature] |
✓ |
1.102 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
1.217 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
1.253 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.086 |
|
|
\[
{}3 y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.990 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.997 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.320 |
|
|
\[
{}y^{\prime \prime }+2 i y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.071 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.282 |
|
|
\[
{}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.805 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.400 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.425 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.950 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.602 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.590 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.597 |
|