|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\frac {y}{t}+y^{\prime } = 3 \cos \left (2 t \right )
\] |
[_linear] |
✓ |
1.625 |
|
|
\[
{}-2 y+y^{\prime } = 3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.324 |
|
|
\[
{}2 y+t y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.447 |
|
|
\[
{}2 t y+y^{\prime } = 2 t \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
2.684 |
|
|
\[
{}4 t y+\left (t^{2}+1\right ) y^{\prime } = \frac {1}{\left (t^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
2.357 |
|
|
\[
{}y+2 y^{\prime } = 3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.240 |
|
|
\[
{}-y+t y^{\prime } = t^{2} {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.427 |
|
|
\[
{}y+y^{\prime } = 5 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.471 |
|
|
\[
{}y+2 y^{\prime } = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.290 |
|
|
\[
{}-y+y^{\prime } = 2 \,{\mathrm e}^{2 t} t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.584 |
|
|
\[
{}2 y+y^{\prime } = t \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.108 |
|
|
\[
{}2 y+t y^{\prime } = t^{2}-t +1
\] |
[_linear] |
✓ |
1.708 |
|
|
\[
{}\frac {2 y}{t}+y^{\prime } = \frac {\cos \left (t \right )}{t^{2}}
\] |
[_linear] |
✓ |
1.753 |
|
|
\[
{}-2 y+y^{\prime } = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.517 |
|
|
\[
{}2 y+t y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.898 |
|
|
\[
{}4 t^{2} y+t^{3} y^{\prime } = {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.670 |
|
|
\[
{}\left (1+t \right ) y+t y^{\prime } = t
\] |
[_linear] |
✓ |
1.500 |
|
|
\[
{}-\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.559 |
|
|
\[
{}-y+2 y^{\prime } = {\mathrm e}^{\frac {t}{3}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.480 |
|
|
\[
{}-2 y+3 y^{\prime } = {\mathrm e}^{-\frac {\pi t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.651 |
|
|
\[
{}\left (1+t \right ) y+t y^{\prime } = 2 t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
2.114 |
|
|
\[
{}2 y+t y^{\prime } = \frac {\sin \left (t \right )}{t}
\] |
[_linear] |
✓ |
1.627 |
|
|
\[
{}\cos \left (t \right ) y+\sin \left (t \right ) y^{\prime } = {\mathrm e}^{t}
\] |
[_linear] |
✓ |
38.844 |
|
|
\[
{}\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.765 |
|
|
\[
{}\frac {2 y}{3}+y^{\prime } = 1-\frac {t}{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.330 |
|
|
\[
{}\frac {y}{4}+y^{\prime } = 3+2 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.077 |
|
|
\[
{}-y+y^{\prime } = 1+3 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.508 |
|
|
\[
{}-\frac {3 y}{2}+y^{\prime } = 2 \,{\mathrm e}^{t}+3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.661 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y}
\] |
[_separable] |
✓ |
2.441 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{\left (x^{3}+1\right ) y}
\] |
[_separable] |
✓ |
1.554 |
|
|
\[
{}\sin \left (x \right ) y^{2}+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.819 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}-1}{3+2 y}
\] |
[_separable] |
✓ |
1.533 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )^{2} \cos \left (2 y\right )^{2}
\] |
[_separable] |
✓ |
2.424 |
|
|
\[
{}y^{\prime } x = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
1.895 |
|
|
\[
{}y^{\prime } = \frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.848 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{1+y^{2}}
\] |
[_separable] |
✓ |
1.219 |
|
|
\[
{}y^{\prime } = \left (1-2 x \right ) y^{2}
\] |
[_separable] |
✓ |
2.078 |
|
|
\[
{}y^{\prime } = \frac {1-2 x}{y}
\] |
[_separable] |
✓ |
4.382 |
|
|
\[
{}x +y y^{\prime } {\mathrm e}^{-x} = 0
\] |
[_separable] |
✓ |
3.675 |
|
|
\[
{}r^{\prime } = \frac {r^{2}}{x}
\] |
[_separable] |
✓ |
2.093 |
|
|
\[
{}y^{\prime } = \frac {2 x}{y+x^{2} y}
\] |
[_separable] |
✓ |
2.259 |
|
|
\[
{}y^{\prime } = \frac {x y^{2}}{\sqrt {x^{2}+1}}
\] |
[_separable] |
✓ |
2.782 |
|
|
\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
[_separable] |
✓ |
3.519 |
|
|
\[
{}y^{\prime } = \frac {x \left (x^{2}+1\right )}{4 y^{3}}
\] |
[_separable] |
✓ |
2.690 |
|
|
\[
{}y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y}
\] |
[_separable] |
✓ |
3.093 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y}
\] |
[_separable] |
✓ |
3.556 |
|
|
\[
{}\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
38.413 |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{2} y^{\prime } = \arcsin \left (x \right )
\] |
[_separable] |
✓ |
5.461 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}+1}{-6 y+3 y^{2}}
\] |
[_separable] |
✓ |
3.773 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}}{-4+3 y^{2}}
\] |
[_separable] |
✓ |
2.561 |
|
|
\[
{}y^{\prime } = 2 y^{2}+x y^{2}
\] |
[_separable] |
✓ |
2.128 |
|
|
\[
{}y^{\prime } = \frac {2-{\mathrm e}^{x}}{3+2 y}
\] |
[_separable] |
✓ |
3.159 |
|
|
\[
{}y^{\prime } = \frac {2 \cos \left (2 x \right )}{3+2 y}
\] |
[_separable] |
✓ |
11.514 |
|
|
\[
{}y^{\prime } = 2 \left (x +1\right ) \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.987 |
|
|
\[
{}y^{\prime } = \frac {t \left (4-y\right ) y}{3}
\] |
[_separable] |
✓ |
2.277 |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{1+t}
\] |
[_separable] |
✓ |
2.814 |
|
|
\[
{}y^{\prime } = \frac {b +a y}{d +c y}
\] |
[_quadrature] |
✓ |
1.404 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.566 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+3 y^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.346 |
|
|
\[
{}y^{\prime } = \frac {4 y-3 x}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.510 |
|
|
\[
{}y^{\prime } = -\frac {4 x +3 y}{2 x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.372 |
|
|
\[
{}y^{\prime } = \frac {x +3 y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.121 |
|
|
\[
{}x^{2}+3 x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.193 |
|
|
\[
{}y^{\prime } = \frac {x^{2}-3 y^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.367 |
|
|
\[
{}y^{\prime } = \frac {3 y^{2}-x^{2}}{2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
75.289 |
|
|
\[
{}\ln \left (t \right ) y+\left (-3+t \right ) y^{\prime } = 2 t
\] |
[_linear] |
✓ |
2.542 |
|
|
\[
{}y+\left (t -4\right ) t y^{\prime } = 0
\] |
[_separable] |
✓ |
2.031 |
|
|
\[
{}\tan \left (t \right ) y+y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.982 |
|
|
\[
{}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2}
\] |
[_linear] |
✓ |
2.171 |
|
|
\[
{}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2}
\] |
[_linear] |
✓ |
1.991 |
|
|
\[
{}y+\ln \left (t \right ) y^{\prime } = \cot \left (t \right )
\] |
[_linear] |
✓ |
2.160 |
|
|
\[
{}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}}
\] |
[_separable] |
✓ |
1.415 |
|
|
\[
{}y^{\prime } = \frac {\cot \left (t \right ) y}{1+y}
\] |
[_separable] |
✓ |
1.637 |
|
|
\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
[_separable] |
✓ |
3.434 |
|
|
\[
{}y^{\prime } = 2 t y^{2}
\] |
[_separable] |
✓ |
1.948 |
|
|
\[
{}y^{3}+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
1.510 |
|
|
\[
{}y^{\prime } = \frac {t^{2}}{\left (t^{3}+1\right ) y}
\] |
[_separable] |
✓ |
1.561 |
|
|
\[
{}y^{\prime } = t \left (3-y\right ) y
\] |
[_separable] |
✓ |
2.227 |
|
|
\[
{}y^{\prime } = y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
1.579 |
|
|
\[
{}y^{\prime } = -y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
1.612 |
|
|
\[
{}y^{\prime } = t -1-y^{2}
\] |
[_Riccati] |
✓ |
1.130 |
|
|
\[
{}y^{\prime } = a y+b y^{2}
\] |
[_quadrature] |
✓ |
1.339 |
|
|
\[
{}y^{\prime } = y \left (-2+y\right ) \left (-1+y\right )
\] |
[_quadrature] |
✓ |
219.769 |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
1.780 |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
1.668 |
|
|
\[
{}y^{\prime } = -\frac {2 \arctan \left (y\right )}{1+y^{2}}
\] |
[_quadrature] |
✓ |
1.924 |
|
|
\[
{}y^{\prime } = -k \left (-1+y\right )^{2}
\] |
[_quadrature] |
✓ |
0.668 |
|
|
\[
{}y^{\prime } = y^{2} \left (y^{2}-1\right )
\] |
[_quadrature] |
✓ |
1.592 |
|
|
\[
{}y^{\prime } = y \left (1-y^{2}\right )
\] |
[_quadrature] |
✓ |
3.791 |
|
|
\[
{}y^{\prime } = -b \sqrt {y}+a y
\] |
[_quadrature] |
✓ |
2.355 |
|
|
\[
{}y^{\prime } = y^{2} \left (4-y^{2}\right )
\] |
[_quadrature] |
✓ |
1.677 |
|
|
\[
{}y^{\prime } = \left (1-y\right )^{2} y^{2}
\] |
[_quadrature] |
✓ |
1.631 |
|
|
\[
{}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.176 |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.264 |
|
|
\[
{}2+3 x^{2}-2 x y+\left (3-x^{2}+6 y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.385 |
|
|
\[
{}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.156 |
|
|
\[
{}y^{\prime } = \frac {-a x -b y}{b x +c y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.767 |
|
|
\[
{}y^{\prime } = \frac {-a x +b y}{b x -c y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.447 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )-2 \sin \left (x \right ) y+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
7.092 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✗ |
8.426 |
|