|
# |
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] |
✓ |
36.912 |
|
|
\[
{}\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.486 |
|
|
\[
{}x \ln \left (x \right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.258 |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
4.680 |
|
|
\[
{}2 x -y+\left (-x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.585 |
|
|
\[
{}-1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.887 |
|
|
\[
{}x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.633 |
|
|
\[
{}y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.226 |
|
|
\[
{}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.204 |
|
|
\[
{}2 x y+3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
2.164 |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{2 x}+y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.293 |
|
|
\[
{}1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.456 |
|
|
\[
{}y+\left (-{\mathrm e}^{-2 y}+2 x y\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.747 |
|
|
\[
{}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.506 |
|
|
\[
{}\frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.411 |
|
|
\[
{}3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.461 |
|
|
\[
{}3 x y+y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.878 |
|
|
\[
{}y^{\prime } = \frac {x^{3}-2 y}{x}
\] |
[_linear] |
✓ |
1.644 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (x \right )+1}{2-\sin \left (y\right )}
\] |
[_separable] |
✓ |
3.046 |
|
|
\[
{}y^{\prime } = \frac {2 x +y}{3-x +3 y^{2}}
\] |
[_rational] |
✓ |
3.790 |
|
|
\[
{}y^{\prime } = 3-6 x +y-2 x y
\] |
[_separable] |
✓ |
1.592 |
|
|
\[
{}y^{\prime } = \frac {-1-2 x y-y^{2}}{x^{2}+2 x y}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.304 |
|
|
\[
{}x y+y^{\prime } x = 1-y
\] |
[_linear] |
✓ |
1.426 |
|
|
\[
{}y^{\prime } = \frac {4 x^{3}+1}{y \left (2+3 y\right )}
\] |
[_separable] |
✓ |
1.513 |
|
|
\[
{}2 y+y^{\prime } x = \frac {\sin \left (x \right )}{x}
\] |
[_linear] |
✓ |
1.689 |
|
|
\[
{}y^{\prime } = \frac {-1-2 x y}{x^{2}+2 y}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.188 |
|
|
\[
{}\frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{-2+y} = 0
\] |
[_separable] |
✓ |
1.665 |
|
|
\[
{}x^{2}+y+\left ({\mathrm e}^{y}+x \right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.512 |
|
|
\[
{}y+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}}
\] |
[_linear] |
✓ |
1.642 |
|
|
\[
{}y^{\prime } = 1+2 x +y^{2}+2 x y^{2}
\] |
[_separable] |
✓ |
2.390 |
|
|
\[
{}x +y+\left (x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.607 |
|
|
\[
{}\left (1+{\mathrm e}^{x}\right ) y^{\prime } = y-y \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
2.244 |
|
|
\[
{}y^{\prime } = \frac {-{\mathrm e}^{2 y} \cos \left (x \right )+\cos \left (y\right ) {\mathrm e}^{-x}}{2 \,{\mathrm e}^{2 y} \sin \left (x \right )-\sin \left (y\right ) {\mathrm e}^{-x}}
\] |
[NONE] |
✓ |
40.761 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x}+3 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.302 |
|
|
\[
{}2 y+y^{\prime } = {\mathrm e}^{-x^{2}-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.331 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}-2 y-y^{3}}{2 x +3 x y^{2}}
\] |
[_rational] |
✓ |
1.416 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y}
\] |
[_separable] |
✓ |
2.417 |
|
|
\[
{}\frac {-4+6 x y+2 y^{2}}{3 x^{2}+4 x y+3 y^{2}}+y^{\prime } = 0
\] |
[_rational] |
✓ |
1.500 |
|
|
\[
{}y^{\prime } = \frac {x^{2}-1}{1+y^{2}}
\] |
[_separable] |
✓ |
3.370 |
|
|
\[
{}\left (1+t \right ) y+t y^{\prime } = {\mathrm e}^{2 t}
\] |
[_linear] |
✓ |
1.392 |
|
|
\[
{}2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.954 |
|
|
\[
{}\frac {2 x}{y}-\frac {y}{x^{2}+y^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{x^{2}+y^{2}}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.985 |
|
|
\[
{}y^{\prime } x = {\mathrm e}^{\frac {y}{x}} x +y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.360 |
|
|
\[
{}y^{\prime } = \frac {x}{x^{2}+y+y^{3}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.358 |
|
|
\[
{}3 t +2 y = -t y^{\prime }
\] |
[_linear] |
✓ |
2.483 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.585 |
|
|
\[
{}2 x y+3 y^{2}-\left (x^{2}+2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.207 |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 x y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.794 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.098 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.080 |
|
|
\[
{}6 y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.093 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.133 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.012 |
|
|
\[
{}4 y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.487 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.382 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.269 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.709 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.688 |
|
|
\[
{}6 y^{\prime \prime }-5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.388 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.509 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.829 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.802 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.730 |
|
|
\[
{}4 y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.904 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.820 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.396 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.158 |
|
|
\[
{}4 y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.299 |
|
|
\[
{}y^{\prime \prime }-\left (2 \alpha -1\right ) y^{\prime }+\alpha \left (\alpha -1\right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.720 |
|
|
\[
{}y^{\prime \prime }+\left (3-\alpha \right ) y^{\prime }-2 \left (\alpha -1\right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
42.911 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.216 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.143 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.559 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.278 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.094 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.540 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.028 |
|
|
\[
{}4 y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.325 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.803 |
|
|
\[
{}9 y^{\prime \prime }+9 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.114 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.586 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.885 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.038 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.328 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.139 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.368 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.460 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.493 |
|
|
\[
{}u^{\prime \prime }-u^{\prime }+2 u = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.498 |
|
|
\[
{}5 u^{\prime \prime }+2 u^{\prime }+7 u = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.316 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.374 |
|
|
\[
{}y^{\prime \prime }+2 a y^{\prime }+\left (a^{2}+1\right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.319 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.287 |
|
|
\[
{}t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.339 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.037 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.243 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.154 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.464 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.148 |
|
|
\[
{}t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.994 |
|