|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.700 |
|
|
\[
{}y^{\prime \prime } = -\frac {1}{2 {y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
2.915 |
|
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
206.677 |
|
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
99.549 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1} \\ y_{2}^{\prime }=y_{1}+y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.399 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=6 y_{1}+y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.515 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}+y_{2}+{\mathrm e}^{3 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.526 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+x y_{3} \\ y_{2}^{\prime }=y_{2}+x^{3} y_{3} \\ y_{3}^{\prime }=2 x y_{1}-y_{2}+{\mathrm e}^{x} y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.053 |
|
|
\[
{}y^{\prime } = 2 x
\] |
[_quadrature] |
✓ |
0.224 |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
1.406 |
|
|
\[
{}y y^{\prime } = {\mathrm e}^{2 x}
\] |
[_separable] |
✓ |
1.181 |
|
|
\[
{}y^{\prime } = k y
\] |
[_quadrature] |
✓ |
0.383 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.764 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.978 |
|
|
\[
{}y^{\prime } x +y = y^{\prime } \sqrt {1-x^{2} y^{2}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.236 |
|
|
\[
{}y^{\prime } x = y+x^{2}+y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.796 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.604 |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.408 |
|
|
\[
{}y^{\prime } x +y = x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.925 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{y x -x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.919 |
|
|
\[
{}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.492 |
|
|
\[
{}1+y^{2}+y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.457 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x}-x
\] |
[_quadrature] |
✓ |
0.266 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.272 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.312 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.330 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \arctan \left (x \right )
\] |
[_quadrature] |
✓ |
0.381 |
|
|
\[
{}y^{\prime } x = 1
\] |
[_quadrature] |
✓ |
0.279 |
|
|
\[
{}y^{\prime } = \arcsin \left (x \right )
\] |
[_quadrature] |
✓ |
0.273 |
|
|
\[
{}\sin \left (x \right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.428 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.579 |
|
|
\[
{}\left (x^{2}-3 x +2\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.366 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.430 |
|
|
\[
{}y^{\prime } = 2 \sin \left (x \right ) \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.487 |
|
|
\[
{}y^{\prime } = \ln \left (x \right )
\] |
[_quadrature] |
✓ |
0.440 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.443 |
|
|
\[
{}x \left (x^{2}-4\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.549 |
|
|
\[
{}\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime } = 2 x^{2}+x
\] |
[_quadrature] |
✓ |
0.961 |
|
|
\[
{}y^{\prime } = 2 y x +1
\] |
[_linear] |
✓ |
0.921 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.804 |
|
|
\[
{}y^{\prime } = \frac {2 x y^{2}}{1-x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.419 |
|
|
\[
{}2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.071 |
|
|
\[
{}x^{5} y^{\prime }+y^{5} = 0
\] |
[_separable] |
✓ |
4.743 |
|
|
\[
{}y^{\prime } = 4 y x
\] |
[_separable] |
✓ |
1.132 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.320 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+1+y^{2} = 0
\] |
[_separable] |
✓ |
1.730 |
|
|
\[
{}y \ln \left (y\right )-y^{\prime } x = 0
\] |
[_separable] |
✓ |
1.490 |
|
|
\[
{}y^{\prime } x = \left (-4 x^{2}+1\right ) \tan \left (y\right )
\] |
[_separable] |
✓ |
1.893 |
|
|
\[
{}y^{\prime } \sin \left (y\right ) = x^{2}
\] |
[_separable] |
✓ |
1.260 |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.261 |
|
|
\[
{}x y y^{\prime } = -1+y
\] |
[_separable] |
✓ |
1.249 |
|
|
\[
{}x y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.179 |
|
|
\[
{}y y^{\prime } = x +1
\] |
[_separable] |
✓ |
2.569 |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
1.420 |
|
|
\[
{}\frac {y^{\prime }}{x^{2}+1} = \frac {x}{y}
\] |
[_separable] |
✓ |
1.090 |
|
|
\[
{}y^{2} y^{\prime } = x +2
\] |
[_separable] |
✓ |
1.290 |
|
|
\[
{}y^{\prime } = x^{2} y^{2}
\] |
[_separable] |
✓ |
1.909 |
|
|
\[
{}y^{\prime } \left (1+y\right ) = -x^{2}+1
\] |
[_separable] |
✓ |
1.153 |
|
|
\[
{}\frac {y^{\prime \prime }}{y^{\prime }} = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.564 |
|
|
\[
{}y^{\prime \prime } y^{\prime } = x \left (x +1\right )
\] |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.365 |
|
|
\[
{}y^{\prime }-y x = 0
\] |
[_separable] |
✓ |
0.135 |
|
|
\[
{}y^{\prime }+y x = x
\] |
[_separable] |
✓ |
0.338 |
|
|
\[
{}y^{\prime }+y = \frac {1}{1+{\mathrm e}^{2 x}}
\] |
[_linear] |
✓ |
0.167 |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.166 |
|
|
\[
{}2 y-x^{3} = y^{\prime } x
\] |
[_linear] |
✓ |
0.132 |
|
|
\[
{}y^{\prime }+2 y x = 0
\] |
[_separable] |
✓ |
0.133 |
|
|
\[
{}y^{\prime } x -3 y = x^{4}
\] |
[_linear] |
✓ |
0.143 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 y x = \cot \left (x \right )
\] |
[_linear] |
✓ |
0.157 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right )
\] |
[_linear] |
✓ |
0.185 |
|
|
\[
{}y-x +x y \cot \left (x \right )+y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.195 |
|
|
\[
{}y^{\prime }-y x = 0
\] |
[_separable] |
✓ |
0.253 |
|
|
\[
{}y^{\prime }-2 y x = 6 x \,{\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
0.309 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y = 3 x^{3}
\] |
[_linear] |
✗ |
0.212 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
0.237 |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.273 |
|
|
\[
{}x^{2} y^{\prime }+y x = 2 x
\] |
[_separable] |
✓ |
0.255 |
|
|
\[
{}y^{\prime } x +y = x^{4} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.252 |
|
|
\[
{}x y^{2} y^{\prime }+y^{3} = x \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
66.912 |
|
|
\[
{}y^{\prime } x +y = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.270 |
|
|
\[
{}y^{\prime }+y x = x y^{4}
\] |
[_separable] |
✓ |
2.256 |
|
|
\[
{}\left ({\mathrm e}^{y}-2 y x \right ) y^{\prime } = y^{2}
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.085 |
|
|
\[
{}y-y^{\prime } x = y^{\prime } y^{2} {\mathrm e}^{y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.075 |
|
|
\[
{}y^{\prime } x +2 = x^{3} \left (-1+y\right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.216 |
|
|
\[
{}y^{\prime } x = 2 x^{2} y+y \ln \left (x \right )
\] |
[_separable] |
✓ |
1.648 |
|
|
\[
{}y^{\prime } \sin \left (2 x \right ) = 2 y+2 \cos \left (x \right )
\] |
[_linear] |
✓ |
3.499 |
|
|
\[
{}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.260 |
|
|
\[
{}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
72.365 |
|
|
\[
{}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.136 |
|
|
\[
{}2 y^{2}-4 x +5 = \left (4-2 y+4 y x \right ) y^{\prime }
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.920 |
|
|
\[
{}y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.416 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.947 |
|
|
\[
{}\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right )
\] |
[_exact] |
✓ |
54.359 |
|
|
\[
{}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
0.242 |
|
|
\[
{}1+y+\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.295 |
|
|
\[
{}2 x y^{3}+\cos \left (x \right ) y+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
81.296 |
|
|
\[
{}\frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}} = 1
\] |
[_exact, _rational, _Riccati] |
✓ |
1.254 |
|
|
\[
{}2 x y^{4}+\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.814 |
|
|
\[
{}\frac {y^{\prime } x +y}{1-x^{2} y^{2}}+x = 0
\] |
[_exact, _rational, _Riccati] |
✓ |
1.573 |
|
|
\[
{}2 x \left (1+\sqrt {x^{2}-y}\right ) = \sqrt {x^{2}-y}\, y^{\prime }
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.670 |
|
|
\[
{}x \ln \left (y\right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.833 |
|