|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{2 y^{\prime }}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.619 |
|
|
\[
{}x y^{\prime \prime \prime } = 2
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.198 |
|
|
\[
{}y^{\prime \prime } = a^{2} y
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.299 |
|
|
\[
{}y^{\prime \prime } = \frac {a}{y^{3}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.131 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.352 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.434 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \sin \left (2 x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.676 |
|
|
\[
{}{y^{\prime \prime }}^{2}+{y^{\prime }}^{2} = a^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.074 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{2 y^{\prime }}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.631 |
|
|
\[
{}y^{\prime \prime \prime } = {y^{\prime \prime }}^{2}
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.199 |
|
|
\[
{}y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2} = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.354 |
|
|
\[
{}y^{\prime \prime } = 9 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.119 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.832 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.930 |
|
|
\[
{}y^{\prime \prime }+12 y = 7 y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.799 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.843 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.791 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.086 |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.868 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.082 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\left (5\right )}-4 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.087 |
|
|
\[
{}y^{\prime \prime \prime \prime }-a^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.052 |
|
|
\[
{}s^{\prime \prime }-a^{2} s = t +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.167 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 8 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.514 |
|
|
\[
{}y^{\prime \prime }-y = 5 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.119 |
|
|
\[
{}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.872 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.031 |
|
|
\[
{}y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.776 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = 2-6 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.568 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+3 y = {\mathrm e}^{-x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.021 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.698 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 2 x +3
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime \prime \prime }-a^{4} y = 5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.164 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 8 \cos \left (a x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.093 |
|
|
\[
{}y^{\prime \prime }+2 h y^{\prime }+n^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.212 |
|
|
\[
{}y^{\prime \prime }+n^{2} y = h \sin \left (r x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.651 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.352 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.785 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\cos \left (2 x \right )^{{3}/{2}}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.353 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+1 \\ y^{\prime }=1+x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.573 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.418 |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }-y^{\prime }+3 x=\sin \left (t \right ) \\ x^{\prime }+y=\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.614 |
|
|
\[
{}y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.018 |
|
|
\[
{}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0
\] |
[_separable] |
✓ |
2.243 |
|
|
\[
{}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.509 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.702 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-x y-\alpha = 0
\] |
[_linear] |
✓ |
1.923 |
|
|
\[
{}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.721 |
|
|
\[
{}y^{\prime \prime }-4 y = {\mathrm e}^{2 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.783 |
|
|
\[
{}x y^{\prime }+y-y^{2} \ln \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
1.990 |
|
|
\[
{}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.306 |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.089 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-3 y \\ y^{\prime }=5 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.622 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-10 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.426 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=12 x+18 y \\ y^{\prime }=-8 x-12 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.268 |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.797 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.338 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=-x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.430 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.375 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.519 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+2 y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.533 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=2 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.514 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.324 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.614 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.287 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.310 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.304 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.344 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=2 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.453 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.211 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.262 |
|
|
\[
{}x^{\prime \prime }+x-x^{3} = 0
\] |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.368 |
|
|
\[
{}x^{\prime \prime }+x+x^{3} = 0
\] |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.749 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x-x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.490 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x+x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.482 |
|
|
\[
{}x^{\prime \prime } = \left (2 \cos \left (x\right )-1\right ) \sin \left (x\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.589 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.383 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.253 |
|
|
\[
{}-y+x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.248 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.229 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.790 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.864 |
|
|
\[
{}y^{\prime }+\frac {1}{2 y} = 0
\] |
[_quadrature] |
✓ |
1.317 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 1
\] |
[_linear] |
✓ |
1.213 |
|
|
\[
{}y^{\prime }-2 \sqrt {{| y|}} = 0
\] |
[_quadrature] |
✓ |
1.543 |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
1.651 |
|
|
\[
{}y^{\prime }-y^{2} = 1
\] |
[_quadrature] |
✓ |
0.953 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.186 |
|
|
\[
{}x y^{\prime }-\sin \left (x \right ) = 0
\] |
[_quadrature] |
✓ |
0.355 |
|
|
\[
{}y^{\prime }+3 y = 0
\] |
[_quadrature] |
✓ |
1.033 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.829 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.823 |
|