|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x -2 \,{\mathrm e}^{x y} \sin \left (2 x \right )+{\mathrm e}^{x y} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{x y} x \cos \left (2 x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
37.423 |
|
|
\[
{}\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.574 |
|
|
\[
{}\ln \left (x \right ) x +x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.383 |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
4.030 |
|
|
\[
{}2 x -y+\left (-x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.446 |
|
|
\[
{}-1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.904 |
|
|
\[
{}x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.636 |
|
|
\[
{}y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.299 |
|
|
\[
{}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.569 |
|
|
\[
{}2 x y+3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
2.007 |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{2 x}+y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.350 |
|
|
\[
{}1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.473 |
|
|
\[
{}y+\left (-{\mathrm e}^{-2 y}+2 x y\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.823 |
|
|
\[
{}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
4.233 |
|
|
\[
{}\frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.372 |
|
|
\[
{}3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.361 |
|
|
\[
{}3 x y+y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
62.626 |
|
|
\[
{}y^{\prime } = \frac {x^{3}-2 y}{x}
\] |
[_linear] |
✓ |
1.621 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (x \right )+1}{2-\sin \left (y\right )}
\] |
[_separable] |
✓ |
3.232 |
|
|
\[
{}y^{\prime } = \frac {2 x +y}{3-x +3 y^{2}}
\] |
[_rational] |
✓ |
4.121 |
|
|
\[
{}y^{\prime } = 3-6 x +y-2 x y
\] |
[_separable] |
✓ |
1.590 |
|
|
\[
{}y^{\prime } = \frac {-1-2 x y-y^{2}}{x^{2}+2 x y}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.535 |
|
|
\[
{}x y+x y^{\prime } = 1-y
\] |
[_linear] |
✓ |
1.507 |
|
|
\[
{}y^{\prime } = \frac {4 x^{3}+1}{y \left (2+3 y\right )}
\] |
[_separable] |
✓ |
1.515 |
|
|
\[
{}2 y+x y^{\prime } = \frac {\sin \left (x \right )}{x}
\] |
[_linear] |
✓ |
1.841 |
|
|
\[
{}y^{\prime } = \frac {-1-2 x y}{x^{2}+2 y}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.223 |
|
|
\[
{}\frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{-2+y} = 0
\] |
[_separable] |
✓ |
1.941 |
|
|
\[
{}x^{2}+y+\left ({\mathrm e}^{y}+x \right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.538 |
|
|
\[
{}y+y^{\prime } = \frac {1}{{\mathrm e}^{x}+1}
\] |
[_linear] |
✓ |
1.726 |
|
|
\[
{}y^{\prime } = 1+2 x +y^{2}+2 x y^{2}
\] |
[_separable] |
✓ |
2.275 |
|
|
\[
{}x +y+\left (x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.249 |
|
|
\[
{}\left ({\mathrm e}^{x}+1\right ) y^{\prime } = y-y \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
2.276 |
|
|
\[
{}y^{\prime } = \frac {-{\mathrm e}^{2 y} \cos \left (x \right )+\cos \left (y\right ) {\mathrm e}^{-x}}{2 \,{\mathrm e}^{2 y} \sin \left (x \right )-\sin \left (y\right ) {\mathrm e}^{-x}}
\] |
[NONE] |
✓ |
40.228 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x}+3 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.358 |
|
|
\[
{}2 y+y^{\prime } = {\mathrm e}^{-x^{2}-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.429 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}-2 y-y^{3}}{2 x +3 x y^{2}}
\] |
[_rational] |
✓ |
1.421 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y}
\] |
[_separable] |
✓ |
2.655 |
|
|
\[
{}\frac {-4+6 x y+2 y^{2}}{3 x^{2}+4 x y+3 y^{2}}+y^{\prime } = 0
\] |
[_rational] |
✓ |
1.474 |
|
|
\[
{}y^{\prime } = \frac {x^{2}-1}{1+y^{2}}
\] |
[_separable] |
✓ |
4.296 |
|
|
\[
{}\left (t +1\right ) y+t y^{\prime } = {\mathrm e}^{2 t}
\] |
[_linear] |
✓ |
1.454 |
|
|
\[
{}2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.229 |
|
|
\[
{}\frac {2 x}{y}-\frac {y}{x^{2}+y^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{x^{2}+y^{2}}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.955 |
|
|
\[
{}x y^{\prime } = {\mathrm e}^{\frac {y}{x}} x +y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
202.954 |
|
|
\[
{}y^{\prime } = \frac {x}{x^{2}+y+y^{3}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.365 |
|
|
\[
{}3 t +2 y = -t y^{\prime }
\] |
[_linear] |
✓ |
2.652 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
39.145 |
|
|
\[
{}2 x y+3 y^{2}-\left (x^{2}+2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
116.724 |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 x y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.515 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.856 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.822 |
|
|
\[
{}6 y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.867 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.851 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.913 |
|
|
\[
{}4 y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.091 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.125 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.011 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.421 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.421 |
|
|
\[
{}6 y^{\prime \prime }-5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.186 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.022 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.611 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.620 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.450 |
|
|
\[
{}4 y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.665 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.548 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.175 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.926 |
|
|
\[
{}4 y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.097 |
|
|
\[
{}y^{\prime \prime }-\left (2 \alpha -1\right ) y^{\prime }+\alpha \left (\alpha -1\right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.472 |
|
|
\[
{}y^{\prime \prime }+\left (3-\alpha \right ) y^{\prime }-2 \left (\alpha -1\right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
41.405 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.905 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.878 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.025 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.042 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.862 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.914 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.534 |
|
|
\[
{}4 y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.222 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.646 |
|
|
\[
{}9 y^{\prime \prime }+9 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.839 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.037 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.715 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.132 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.109 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.819 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.119 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.408 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.364 |
|
|
\[
{}u^{\prime \prime }-u^{\prime }+2 u = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.137 |
|
|
\[
{}5 u^{\prime \prime }+2 u^{\prime }+7 u = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.989 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.134 |
|
|
\[
{}y^{\prime \prime }+2 a y^{\prime }+\left (a^{2}+1\right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.084 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.079 |
|
|
\[
{}t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.175 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.826 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.951 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.899 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
4.231 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.878 |
|
|
\[
{}t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.498 |
|