|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\frac {y}{t}+y^{\prime } = 3 \cos \left (2 t \right )
\] |
[_linear] |
✓ |
1.503 |
|
|
\[
{}-2 y+y^{\prime } = 3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.903 |
|
|
\[
{}2 y+t y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.244 |
|
|
\[
{}2 t y+y^{\prime } = 2 t \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
4.234 |
|
|
\[
{}4 t y+\left (t^{2}+1\right ) y^{\prime } = \frac {1}{\left (t^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
1.813 |
|
|
\[
{}y+2 y^{\prime } = 3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
0.824 |
|
|
\[
{}-y+t y^{\prime } = t^{2} {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
0.994 |
|
|
\[
{}y+y^{\prime } = 5 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.219 |
|
|
\[
{}y+2 y^{\prime } = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.916 |
|
|
\[
{}-y+y^{\prime } = 2 \,{\mathrm e}^{2 t} t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.158 |
|
|
\[
{}2 y+y^{\prime } = t \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.518 |
|
|
\[
{}2 y+t y^{\prime } = t^{2}-t +1
\] |
[_linear] |
✓ |
1.369 |
|
|
\[
{}\frac {2 y}{t}+y^{\prime } = \frac {\cos \left (t \right )}{t^{2}}
\] |
[_linear] |
✓ |
3.401 |
|
|
\[
{}-2 y+y^{\prime } = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.887 |
|
|
\[
{}2 y+t y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.382 |
|
|
\[
{}4 t^{2} y+t^{3} y^{\prime } = {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.317 |
|
|
\[
{}\left (1+t \right ) y+t y^{\prime } = t
\] |
[_linear] |
✓ |
1.071 |
|
|
\[
{}-\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
3.289 |
|
|
\[
{}-y+2 y^{\prime } = {\mathrm e}^{\frac {t}{3}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.185 |
|
|
\[
{}-2 y+3 y^{\prime } = {\mathrm e}^{-\frac {\pi t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.476 |
|
|
\[
{}\left (1+t \right ) y+t y^{\prime } = 2 t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.847 |
|
|
\[
{}2 y+t y^{\prime } = \frac {\sin \left (t \right )}{t}
\] |
[_linear] |
✓ |
1.441 |
|
|
\[
{}\cos \left (t \right ) y+\sin \left (t \right ) y^{\prime } = {\mathrm e}^{t}
\] |
[_linear] |
✓ |
75.595 |
|
|
\[
{}\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.348 |
|
|
\[
{}\frac {2 y}{3}+y^{\prime } = 1-\frac {t}{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.970 |
|
|
\[
{}\frac {y}{4}+y^{\prime } = 3+2 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
3.832 |
|
|
\[
{}-y+y^{\prime } = 1+3 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.323 |
|
|
\[
{}-\frac {3 y}{2}+y^{\prime } = 2 \,{\mathrm e}^{t}+3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.076 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y}
\] |
[_separable] |
✓ |
2.313 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{\left (x^{3}+1\right ) y}
\] |
[_separable] |
✓ |
3.198 |
|
|
\[
{}\sin \left (x \right ) y^{2}+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.582 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}-1}{3+2 y}
\] |
[_separable] |
✓ |
1.463 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )^{2} \cos \left (2 y\right )^{2}
\] |
[_separable] |
✓ |
4.605 |
|
|
\[
{}y^{\prime } x = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
2.483 |
|
|
\[
{}y^{\prime } = \frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.151 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{1+y^{2}}
\] |
[_separable] |
✓ |
0.988 |
|
|
\[
{}y^{\prime } = \left (1-2 x \right ) y^{2}
\] |
[_separable] |
✓ |
4.294 |
|
|
\[
{}y^{\prime } = \frac {1-2 x}{y}
\] |
[_separable] |
✓ |
4.284 |
|
|
\[
{}x +y y^{\prime } {\mathrm e}^{-x} = 0
\] |
[_separable] |
✓ |
3.371 |
|
|
\[
{}r^{\prime } = \frac {r^{2}}{x}
\] |
[_separable] |
✓ |
1.670 |
|
|
\[
{}y^{\prime } = \frac {2 x}{y+x^{2} y}
\] |
[_separable] |
✓ |
1.333 |
|
|
\[
{}y^{\prime } = \frac {x y^{2}}{\sqrt {x^{2}+1}}
\] |
[_separable] |
✓ |
4.116 |
|
|
\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
[_separable] |
✓ |
4.239 |
|
|
\[
{}y^{\prime } = \frac {x \left (x^{2}+1\right )}{4 y^{3}}
\] |
[_separable] |
✓ |
3.394 |
|
|
\[
{}y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y}
\] |
[_separable] |
✓ |
1.688 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y}
\] |
[_separable] |
✓ |
1.515 |
|
|
\[
{}\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
91.479 |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{2} y^{\prime } = \arcsin \left (x \right )
\] |
[_separable] |
✓ |
3.774 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}+1}{-6 y+3 y^{2}}
\] |
[_separable] |
✓ |
3.690 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}}{-4+3 y^{2}}
\] |
[_separable] |
✓ |
1.170 |
|
|
\[
{}y^{\prime } = 2 y^{2}+x y^{2}
\] |
[_separable] |
✓ |
2.299 |
|
|
\[
{}y^{\prime } = \frac {2-{\mathrm e}^{x}}{3+2 y}
\] |
[_separable] |
✓ |
3.495 |
|
|
\[
{}y^{\prime } = \frac {2 \cos \left (2 x \right )}{3+2 y}
\] |
[_separable] |
✓ |
2.213 |
|
|
\[
{}y^{\prime } = 2 \left (x +1\right ) \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.286 |
|
|
\[
{}y^{\prime } = \frac {t \left (4-y\right ) y}{3}
\] |
[_separable] |
✓ |
4.957 |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{1+t}
\] |
[_separable] |
✓ |
5.992 |
|
|
\[
{}y^{\prime } = \frac {b +a y}{d +c y}
\] |
[_quadrature] |
✓ |
0.918 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+y x +y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.440 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+3 y^{2}}{2 y x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
11.740 |
|
|
\[
{}y^{\prime } = \frac {4 y-3 x}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.686 |
|
|
\[
{}y^{\prime } = -\frac {4 x +3 y}{2 x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
20.324 |
|
|
\[
{}y^{\prime } = \frac {x +3 y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.634 |
|
|
\[
{}x^{2}+3 y x +y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.142 |
|
|
\[
{}y^{\prime } = \frac {x^{2}-3 y^{2}}{2 y x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
11.909 |
|
|
\[
{}y^{\prime } = \frac {3 y^{2}-x^{2}}{2 y x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
87.025 |
|
|
\[
{}\ln \left (t \right ) y+\left (-3+t \right ) y^{\prime } = 2 t
\] |
[_linear] |
✓ |
3.420 |
|
|
\[
{}y+\left (-4+t \right ) t y^{\prime } = 0
\] |
[_separable] |
✓ |
4.493 |
|
|
\[
{}\tan \left (t \right ) y+y^{\prime } = \sin \left (t \right )
\] |
[_linear] |
✓ |
2.059 |
|
|
\[
{}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2}
\] |
[_linear] |
✓ |
1.796 |
|
|
\[
{}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2}
\] |
[_linear] |
✓ |
1.598 |
|
|
\[
{}y+\ln \left (t \right ) y^{\prime } = \cot \left (t \right )
\] |
[_linear] |
✓ |
4.299 |
|
|
\[
{}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}}
\] |
[_separable] |
✓ |
1.442 |
|
|
\[
{}y^{\prime } = \frac {\cot \left (t \right ) y}{1+y}
\] |
[_separable] |
✓ |
2.044 |
|
|
\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
[_separable] |
✓ |
10.213 |
|
|
\[
{}y^{\prime } = 2 t y^{2}
\] |
[_separable] |
✓ |
2.464 |
|
|
\[
{}y^{3}+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.801 |
|
|
\[
{}y^{\prime } = \frac {t^{2}}{\left (t^{3}+1\right ) y}
\] |
[_separable] |
✓ |
3.616 |
|
|
\[
{}y^{\prime } = t \left (3-y\right ) y
\] |
[_separable] |
✓ |
3.115 |
|
|
\[
{}y^{\prime } = y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
4.766 |
|
|
\[
{}y^{\prime } = -y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
2.348 |
|
|
\[
{}y^{\prime } = t -1-y^{2}
\] |
[_Riccati] |
✓ |
3.578 |
|
|
\[
{}y^{\prime } = a y+b y^{2}
\] |
[_quadrature] |
✓ |
1.484 |
|
|
\[
{}y^{\prime } = y \left (-2+y\right ) \left (y-1\right )
\] |
[_quadrature] |
✓ |
3.135 |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
0.990 |
|
|
\[
{}y^{\prime } = -1+{\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
1.097 |
|
|
\[
{}y^{\prime } = -\frac {2 \arctan \left (y\right )}{1+y^{2}}
\] |
[_quadrature] |
✓ |
2.944 |
|
|
\[
{}y^{\prime } = -k \left (y-1\right )^{2}
\] |
[_quadrature] |
✓ |
0.373 |
|
|
\[
{}y^{\prime } = y^{2} \left (y^{2}-1\right )
\] |
[_quadrature] |
✓ |
3.336 |
|
|
\[
{}y^{\prime } = y \left (1-y^{2}\right )
\] |
[_quadrature] |
✓ |
3.929 |
|
|
\[
{}y^{\prime } = -b \sqrt {y}+a y
\] |
[_quadrature] |
✓ |
4.388 |
|
|
\[
{}y^{\prime } = y^{2} \left (4-y^{2}\right )
\] |
[_quadrature] |
✓ |
1.158 |
|
|
\[
{}y^{\prime } = \left (1-y\right )^{2} y^{2}
\] |
[_quadrature] |
✓ |
0.735 |
|
|
\[
{}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
7.130 |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
26.793 |
|
|
\[
{}2+3 x^{2}-2 y x +\left (3-x^{2}+6 y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
3.907 |
|
|
\[
{}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.017 |
|
|
\[
{}y^{\prime } = \frac {-a x -b y}{b x +c y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
13.472 |
|
|
\[
{}y^{\prime } = \frac {-a x +b y}{b x -c y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.296 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )-2 \sin \left (x \right ) y+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
18.385 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✗ |
4.208 |
|