|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\frac {y}{t}+y^{\prime } = 3 \cos \left (2 t \right )
\] |
[_linear] |
✓ |
1.637 |
|
|
\[
{}-2 y+y^{\prime } = 3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.368 |
|
|
\[
{}2 y+t y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.506 |
|
|
\[
{}2 t y+y^{\prime } = 2 t \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
2.727 |
|
|
\[
{}4 t y+\left (t^{2}+1\right ) y^{\prime } = \frac {1}{\left (t^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
2.380 |
|
|
\[
{}y+2 y^{\prime } = 3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.286 |
|
|
\[
{}-y+t y^{\prime } = t^{2} {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.487 |
|
|
\[
{}y+y^{\prime } = 5 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.623 |
|
|
\[
{}y+2 y^{\prime } = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.342 |
|
|
\[
{}-y+y^{\prime } = 2 \,{\mathrm e}^{2 t} t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.643 |
|
|
\[
{}2 y+y^{\prime } = t \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.129 |
|
|
\[
{}2 y+t y^{\prime } = t^{2}-t +1
\] |
[_linear] |
✓ |
1.825 |
|
|
\[
{}\frac {2 y}{t}+y^{\prime } = \frac {\cos \left (t \right )}{t^{2}}
\] |
[_linear] |
✓ |
1.724 |
|
|
\[
{}-2 y+y^{\prime } = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.524 |
|
|
\[
{}2 y+t y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.895 |
|
|
\[
{}4 t^{2} y+t^{3} y^{\prime } = {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.618 |
|
|
\[
{}\left (t +1\right ) y+t y^{\prime } = t
\] |
[_linear] |
✓ |
1.536 |
|
|
\[
{}-\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.621 |
|
|
\[
{}-y+2 y^{\prime } = {\mathrm e}^{\frac {t}{3}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.461 |
|
|
\[
{}-2 y+3 y^{\prime } = {\mathrm e}^{-\frac {\pi t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.728 |
|
|
\[
{}\left (t +1\right ) y+t y^{\prime } = 2 t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
2.246 |
|
|
\[
{}2 y+t y^{\prime } = \frac {\sin \left (t \right )}{t}
\] |
[_linear] |
✓ |
1.655 |
|
|
\[
{}\cos \left (t \right ) y+\sin \left (t \right ) y^{\prime } = {\mathrm e}^{t}
\] |
[_linear] |
✓ |
35.893 |
|
|
\[
{}\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.943 |
|
|
\[
{}\frac {2 y}{3}+y^{\prime } = 1-\frac {t}{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.332 |
|
|
\[
{}\frac {y}{4}+y^{\prime } = 3+2 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.187 |
|
|
\[
{}-y+y^{\prime } = 1+3 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.712 |
|
|
\[
{}-\frac {3 y}{2}+y^{\prime } = 2 \,{\mathrm e}^{t}+3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.499 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y}
\] |
[_separable] |
✓ |
2.191 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{\left (x^{3}+1\right ) y}
\] |
[_separable] |
✓ |
1.901 |
|
|
\[
{}\sin \left (x \right ) y^{2}+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.918 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}-1}{3+2 y}
\] |
[_separable] |
✓ |
1.737 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )^{2} \cos \left (2 y\right )^{2}
\] |
[_separable] |
✓ |
2.527 |
|
|
\[
{}x y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
6.326 |
|
|
\[
{}y^{\prime } = \frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.895 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{1+y^{2}}
\] |
[_separable] |
✓ |
1.292 |
|
|
\[
{}y^{\prime } = \left (1-2 x \right ) y^{2}
\] |
[_separable] |
✓ |
2.308 |
|
|
\[
{}y^{\prime } = \frac {1-2 x}{y}
\] |
[_separable] |
✓ |
3.910 |
|
|
\[
{}x +y y^{\prime } {\mathrm e}^{-x} = 0
\] |
[_separable] |
✓ |
4.357 |
|
|
\[
{}r^{\prime } = \frac {r^{2}}{x}
\] |
[_separable] |
✓ |
2.108 |
|
|
\[
{}y^{\prime } = \frac {2 x}{y+x^{2} y}
\] |
[_separable] |
✓ |
2.369 |
|
|
\[
{}y^{\prime } = \frac {x y^{2}}{\sqrt {x^{2}+1}}
\] |
[_separable] |
✓ |
2.900 |
|
|
\[
{}y^{\prime } = \frac {2 x}{2 y+1}
\] |
[_separable] |
✓ |
3.499 |
|
|
\[
{}y^{\prime } = \frac {x \left (x^{2}+1\right )}{4 y^{3}}
\] |
[_separable] |
✓ |
2.975 |
|
|
\[
{}y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y}
\] |
[_separable] |
✓ |
3.338 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y}
\] |
[_separable] |
✓ |
4.533 |
|
|
\[
{}\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
38.986 |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{2} y^{\prime } = \arcsin \left (x \right )
\] |
[_separable] |
✓ |
3.368 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}+1}{-6 y+3 y^{2}}
\] |
[_separable] |
✓ |
4.862 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}}{-4+3 y^{2}}
\] |
[_separable] |
✓ |
3.079 |
|
|
\[
{}y^{\prime } = 2 y^{2}+x y^{2}
\] |
[_separable] |
✓ |
2.368 |
|
|
\[
{}y^{\prime } = \frac {2-{\mathrm e}^{x}}{3+2 y}
\] |
[_separable] |
✓ |
3.632 |
|
|
\[
{}y^{\prime } = \frac {2 \cos \left (2 x \right )}{3+2 y}
\] |
[_separable] |
✓ |
14.723 |
|
|
\[
{}y^{\prime } = 2 \left (x +1\right ) \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.763 |
|
|
\[
{}y^{\prime } = \frac {t \left (4-y\right ) y}{3}
\] |
[_separable] |
✓ |
2.609 |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{t +1}
\] |
[_separable] |
✓ |
3.117 |
|
|
\[
{}y^{\prime } = \frac {b +a y}{d +c y}
\] |
[_quadrature] |
✓ |
1.974 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.514 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+3 y^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
6.937 |
|
|
\[
{}y^{\prime } = \frac {4 y-3 x}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.009 |
|
|
\[
{}y^{\prime } = -\frac {4 x +3 y}{2 x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.078 |
|
|
\[
{}y^{\prime } = \frac {x +3 y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.358 |
|
|
\[
{}x^{2}+3 x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.224 |
|
|
\[
{}y^{\prime } = \frac {x^{2}-3 y^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
57.382 |
|
|
\[
{}y^{\prime } = \frac {3 y^{2}-x^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
120.224 |
|
|
\[
{}\ln \left (t \right ) y+\left (t -3\right ) y^{\prime } = 2 t
\] |
[_linear] |
✓ |
2.099 |
|
|
\[
{}y+\left (-4+t \right ) t y^{\prime } = 0
\] |
[_separable] |
✓ |
2.068 |
|
|
\[
{}\tan \left (t \right ) y+y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
2.036 |
|
|
\[
{}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2}
\] |
[_linear] |
✓ |
2.257 |
|
|
\[
{}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2}
\] |
[_linear] |
✓ |
2.095 |
|
|
\[
{}y+\ln \left (t \right ) y^{\prime } = \cot \left (t \right )
\] |
[_linear] |
✓ |
1.830 |
|
|
\[
{}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}}
\] |
[_separable] |
✓ |
1.446 |
|
|
\[
{}y^{\prime } = \frac {\cot \left (t \right ) y}{y+1}
\] |
[_separable] |
✓ |
1.897 |
|
|
\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
[_separable] |
✓ |
4.111 |
|
|
\[
{}y^{\prime } = 2 t y^{2}
\] |
[_separable] |
✓ |
2.123 |
|
|
\[
{}y^{3}+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
5.093 |
|
|
\[
{}y^{\prime } = \frac {t^{2}}{\left (t^{3}+1\right ) y}
\] |
[_separable] |
✓ |
1.912 |
|
|
\[
{}y^{\prime } = t \left (3-y\right ) y
\] |
[_separable] |
✓ |
2.583 |
|
|
\[
{}y^{\prime } = y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
1.844 |
|
|
\[
{}y^{\prime } = -y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
1.840 |
|
|
\[
{}y^{\prime } = t -1-y^{2}
\] |
[_Riccati] |
✓ |
1.188 |
|
|
\[
{}y^{\prime } = a y+b y^{2}
\] |
[_quadrature] |
✓ |
3.731 |
|
|
\[
{}y^{\prime } = y \left (-2+y\right ) \left (-1+y\right )
\] |
[_quadrature] |
✓ |
3.837 |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
2.342 |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
2.245 |
|
|
\[
{}y^{\prime } = -\frac {2 \arctan \left (y\right )}{1+y^{2}}
\] |
[_quadrature] |
✓ |
4.915 |
|
|
\[
{}y^{\prime } = -k \left (-1+y\right )^{2}
\] |
[_quadrature] |
✓ |
1.208 |
|
|
\[
{}y^{\prime } = y^{2} \left (-1+y^{2}\right )
\] |
[_quadrature] |
✓ |
1.734 |
|
|
\[
{}y^{\prime } = y \left (1-y^{2}\right )
\] |
[_quadrature] |
✓ |
4.331 |
|
|
\[
{}y^{\prime } = -b \sqrt {y}+a y
\] |
[_quadrature] |
✓ |
4.172 |
|
|
\[
{}y^{\prime } = y^{2} \left (4-y^{2}\right )
\] |
[_quadrature] |
✓ |
1.845 |
|
|
\[
{}y^{\prime } = \left (1-y\right )^{2} y^{2}
\] |
[_quadrature] |
✓ |
1.829 |
|
|
\[
{}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.944 |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.551 |
|
|
\[
{}2+3 x^{2}-2 x y+\left (3-x^{2}+6 y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.369 |
|
|
\[
{}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.209 |
|
|
\[
{}y^{\prime } = \frac {-a x -b y}{b x +c y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.211 |
|
|
\[
{}y^{\prime } = \frac {-a x +b y}{b x -c y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.568 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )-2 \sin \left (x \right ) y+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
7.007 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✗ |
9.158 |
|