|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\frac {y}{t}+y^{\prime } = 3 \cos \left (2 t \right )
\] |
[_linear] |
✓ |
1.464 |
|
|
\[
{}-2 y+y^{\prime } = 3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.155 |
|
|
\[
{}2 y+t y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.542 |
|
|
\[
{}2 t y+y^{\prime } = 2 t \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
2.844 |
|
|
\[
{}4 t y+\left (t^{2}+1\right ) y^{\prime } = \frac {1}{\left (t^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
2.527 |
|
|
\[
{}y+2 y^{\prime } = 3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.175 |
|
|
\[
{}-y+t y^{\prime } = t^{2} {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.270 |
|
|
\[
{}y+y^{\prime } = 5 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.319 |
|
|
\[
{}y+2 y^{\prime } = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.063 |
|
|
\[
{}-y+y^{\prime } = 2 \,{\mathrm e}^{2 t} t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.417 |
|
|
\[
{}2 y+y^{\prime } = t \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.861 |
|
|
\[
{}2 y+t y^{\prime } = t^{2}-t +1
\] |
[_linear] |
✓ |
1.503 |
|
|
\[
{}\frac {2 y}{t}+y^{\prime } = \frac {\cos \left (t \right )}{t^{2}}
\] |
[_linear] |
✓ |
1.575 |
|
|
\[
{}-2 y+y^{\prime } = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.269 |
|
|
\[
{}2 y+t y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.613 |
|
|
\[
{}4 t^{2} y+t^{3} y^{\prime } = {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.541 |
|
|
\[
{}\left (t +1\right ) y+t y^{\prime } = t
\] |
[_linear] |
✓ |
1.326 |
|
|
\[
{}-\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.397 |
|
|
\[
{}-y+2 y^{\prime } = {\mathrm e}^{\frac {t}{3}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.283 |
|
|
\[
{}-2 y+3 y^{\prime } = {\mathrm e}^{-\frac {\pi t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.437 |
|
|
\[
{}\left (t +1\right ) y+t y^{\prime } = 2 t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.954 |
|
|
\[
{}2 y+t y^{\prime } = \frac {\sin \left (t \right )}{t}
\] |
[_linear] |
✓ |
1.471 |
|
|
\[
{}\cos \left (t \right ) y+\sin \left (t \right ) y^{\prime } = {\mathrm e}^{t}
\] |
[_linear] |
✓ |
38.830 |
|
|
\[
{}\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.608 |
|
|
\[
{}\frac {2 y}{3}+y^{\prime } = 1-\frac {t}{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.093 |
|
|
\[
{}\frac {y}{4}+y^{\prime } = 3+2 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.145 |
|
|
\[
{}-y+y^{\prime } = 1+3 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.520 |
|
|
\[
{}-\frac {3 y}{2}+y^{\prime } = 2 \,{\mathrm e}^{t}+3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.415 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y}
\] |
[_separable] |
✓ |
1.893 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{\left (x^{3}+1\right ) y}
\] |
[_separable] |
✓ |
1.357 |
|
|
\[
{}\sin \left (x \right ) y^{2}+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.657 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}-1}{3+2 y}
\] |
[_separable] |
✓ |
1.361 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )^{2} \cos \left (2 y\right )^{2}
\] |
[_separable] |
✓ |
2.384 |
|
|
\[
{}x y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
2.188 |
|
|
\[
{}y^{\prime } = \frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.853 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{1+y^{2}}
\] |
[_separable] |
✓ |
1.118 |
|
|
\[
{}y^{\prime } = \left (-2 x +1\right ) y^{2}
\] |
[_separable] |
✓ |
1.880 |
|
|
\[
{}y^{\prime } = \frac {-2 x +1}{y}
\] |
[_separable] |
✓ |
4.207 |
|
|
\[
{}x +y y^{\prime } {\mathrm e}^{-x} = 0
\] |
[_separable] |
✓ |
3.680 |
|
|
\[
{}r^{\prime } = \frac {r^{2}}{x}
\] |
[_separable] |
✓ |
1.726 |
|
|
\[
{}y^{\prime } = \frac {2 x}{y+x^{2} y}
\] |
[_separable] |
✓ |
2.218 |
|
|
\[
{}y^{\prime } = \frac {x y^{2}}{\sqrt {x^{2}+1}}
\] |
[_separable] |
✓ |
2.589 |
|
|
\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
[_separable] |
✓ |
3.347 |
|
|
\[
{}y^{\prime } = \frac {x \left (x^{2}+1\right )}{4 y^{3}}
\] |
[_separable] |
✓ |
2.632 |
|
|
\[
{}y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y}
\] |
[_separable] |
✓ |
3.079 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y}
\] |
[_separable] |
✓ |
3.569 |
|
|
\[
{}\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
38.169 |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{2} y^{\prime } = \arcsin \left (x \right )
\] |
[_separable] |
✓ |
5.727 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}+1}{-6 y+3 y^{2}}
\] |
[_separable] |
✓ |
3.887 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}}{-4+3 y^{2}}
\] |
[_separable] |
✓ |
2.534 |
|
|
\[
{}y^{\prime } = 2 y^{2}+x y^{2}
\] |
[_separable] |
✓ |
1.890 |
|
|
\[
{}y^{\prime } = \frac {2-{\mathrm e}^{x}}{3+2 y}
\] |
[_separable] |
✓ |
3.220 |
|
|
\[
{}y^{\prime } = \frac {2 \cos \left (2 x \right )}{3+2 y}
\] |
[_separable] |
✓ |
12.114 |
|
|
\[
{}y^{\prime } = 2 \left (x +1\right ) \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.771 |
|
|
\[
{}y^{\prime } = \frac {t \left (4-y\right ) y}{3}
\] |
[_separable] |
✓ |
2.056 |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{t +1}
\] |
[_separable] |
✓ |
2.656 |
|
|
\[
{}y^{\prime } = \frac {a y+b}{d +c y}
\] |
[_quadrature] |
✓ |
1.556 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.203 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+3 y^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.014 |
|
|
\[
{}y^{\prime } = \frac {4 y-3 x}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.661 |
|
|
\[
{}y^{\prime } = -\frac {4 x +3 y}{2 x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.853 |
|
|
\[
{}y^{\prime } = \frac {3 y+x}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.351 |
|
|
\[
{}x^{2}+3 x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.796 |
|
|
\[
{}y^{\prime } = \frac {x^{2}-3 y^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.101 |
|
|
\[
{}y^{\prime } = \frac {3 y^{2}-x^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
75.099 |
|
|
\[
{}\ln \left (t \right ) y+\left (t -3\right ) y^{\prime } = 2 t
\] |
[_linear] |
✓ |
2.754 |
|
|
\[
{}y+\left (-4+t \right ) t y^{\prime } = 0
\] |
[_separable] |
✓ |
1.734 |
|
|
\[
{}\tan \left (t \right ) y+y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.881 |
|
|
\[
{}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2}
\] |
[_linear] |
✓ |
2.087 |
|
|
\[
{}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2}
\] |
[_linear] |
✓ |
1.805 |
|
|
\[
{}y+\ln \left (t \right ) y^{\prime } = \cot \left (t \right )
\] |
[_linear] |
✓ |
2.155 |
|
|
\[
{}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}}
\] |
[_separable] |
✓ |
1.335 |
|
|
\[
{}y^{\prime } = \frac {\cot \left (t \right ) y}{1+y}
\] |
[_separable] |
✓ |
1.566 |
|
|
\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
[_separable] |
✓ |
2.987 |
|
|
\[
{}y^{\prime } = 2 t y^{2}
\] |
[_separable] |
✓ |
1.582 |
|
|
\[
{}y^{3}+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
1.177 |
|
|
\[
{}y^{\prime } = \frac {t^{2}}{\left (t^{3}+1\right ) y}
\] |
[_separable] |
✓ |
1.355 |
|
|
\[
{}y^{\prime } = t \left (3-y\right ) y
\] |
[_separable] |
✓ |
1.994 |
|
|
\[
{}y^{\prime } = y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
1.575 |
|
|
\[
{}y^{\prime } = -y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
1.549 |
|
|
\[
{}y^{\prime } = t -1-y^{2}
\] |
[_Riccati] |
✓ |
1.115 |
|
|
\[
{}y^{\prime } = a y+b y^{2}
\] |
[_quadrature] |
✓ |
1.453 |
|
|
\[
{}y^{\prime } = y \left (-2+y\right ) \left (-1+y\right )
\] |
[_quadrature] |
✓ |
218.093 |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
1.512 |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
1.377 |
|
|
\[
{}y^{\prime } = -\frac {2 \arctan \left (y\right )}{1+y^{2}}
\] |
[_quadrature] |
✓ |
1.686 |
|
|
\[
{}y^{\prime } = -k \left (-1+y\right )^{2}
\] |
[_quadrature] |
✓ |
0.712 |
|
|
\[
{}y^{\prime } = y^{2} \left (y^{2}-1\right )
\] |
[_quadrature] |
✓ |
1.418 |
|
|
\[
{}y^{\prime } = y \left (1-y^{2}\right )
\] |
[_quadrature] |
✓ |
3.674 |
|
|
\[
{}y^{\prime } = -b \sqrt {y}+a y
\] |
[_quadrature] |
✓ |
2.531 |
|
|
\[
{}y^{\prime } = y^{2} \left (4-y^{2}\right )
\] |
[_quadrature] |
✓ |
1.492 |
|
|
\[
{}y^{\prime } = \left (1-y\right )^{2} y^{2}
\] |
[_quadrature] |
✓ |
1.427 |
|
|
\[
{}3+2 x +\left (2 y-2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.644 |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.451 |
|
|
\[
{}2+3 x^{2}-2 x y+\left (3-x^{2}+6 y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.353 |
|
|
\[
{}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.652 |
|
|
\[
{}y^{\prime } = \frac {-a x -b y}{b x +c y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.503 |
|
|
\[
{}y^{\prime } = \frac {-a x +b y}{b x -c y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.079 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )-2 y \sin \left (x \right )+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
6.914 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✗ |
7.996 |
|