| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\frac {y}{t}+y^{\prime }&=3 \cos \left (2 t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.855 |
|
| \begin{align*}
-2 y+y^{\prime }&=3 \,{\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.377 |
|
| \begin{align*}
2 y+y^{\prime } t&=\sin \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.862 |
|
| \begin{align*}
2 t y+y^{\prime }&=2 t \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.503 |
|
| \begin{align*}
4 t y+\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.198 |
|
| \begin{align*}
y+2 y^{\prime }&=3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.412 |
|
| \begin{align*}
-y+y^{\prime } t&={\mathrm e}^{-t} t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.387 |
|
| \begin{align*}
y+y^{\prime }&=5 \sin \left (2 t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.142 |
|
| \begin{align*}
y+2 y^{\prime }&=3 t^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.836 |
|
| \begin{align*}
-y+y^{\prime }&=2 \,{\mathrm e}^{2 t} t \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.038 |
|
| \begin{align*}
2 y+y^{\prime }&=t \,{\mathrm e}^{-2 t} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.784 |
|
| \begin{align*}
2 y+y^{\prime } t&=t^{2}-t +1 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.367 |
|
| \begin{align*}
\frac {2 y}{t}+y^{\prime }&=\frac {\cos \left (t \right )}{t^{2}} \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.374 |
|
| \begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| \begin{align*}
2 y+y^{\prime } t&=\sin \left (t \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.036 |
|
| \begin{align*}
4 t^{2} y+t^{3} y^{\prime }&={\mathrm e}^{-t} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.116 |
|
| \begin{align*}
\left (1+t \right ) y+y^{\prime } t&=t \\
y \left (\ln \left (2\right )\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.751 |
|
| \begin{align*}
-\frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.925 |
|
| \begin{align*}
-y+2 y^{\prime }&={\mathrm e}^{\frac {t}{3}} \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.561 |
|
| \begin{align*}
-2 y+3 y^{\prime }&={\mathrm e}^{-\frac {\pi t}{2}} \\
y \left (0\right ) &= a \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.835 |
|
| \begin{align*}
\left (1+t \right ) y+y^{\prime } t&=2 t \,{\mathrm e}^{-t} \\
y \left (1\right ) &= a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.285 |
|
| \begin{align*}
2 y+y^{\prime } t&=\frac {\sin \left (t \right )}{t} \\
y \left (-\frac {\pi }{2}\right ) &= a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.193 |
|
| \begin{align*}
y \cos \left (t \right )+\sin \left (t \right ) y^{\prime }&={\mathrm e}^{t} \\
y \left (1\right ) &= a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
26.871 |
|
| \begin{align*}
\frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.954 |
|
| \begin{align*}
\frac {2 y}{3}+y^{\prime }&=1-\frac {t}{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.177 |
|
| \begin{align*}
\frac {y}{4}+y^{\prime }&=3+2 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.301 |
|
| \begin{align*}
-y+y^{\prime }&=1+3 \sin \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.927 |
|
| \begin{align*}
-\frac {3 y}{2}+y^{\prime }&=2 \,{\mathrm e}^{t}+3 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.365 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.583 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.091 |
|
| \begin{align*}
\sin \left (x \right ) y^{2}+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.862 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}-1}{3+2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.388 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )^{2} \cos \left (2 y\right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.653 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {1-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.304 |
|
| \begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
2.115 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.663 |
|
| \begin{align*}
y^{\prime }&=\left (1-2 x \right ) y^{2} \\
y \left (0\right ) &= -{\frac {1}{6}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.993 |
|
| \begin{align*}
y^{\prime }&=\frac {1-2 x}{y} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.290 |
|
| \begin{align*}
x +y y^{\prime } {\mathrm e}^{-x}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.232 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}}{x} \\
r \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.944 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{y+x^{2} y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.267 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}}{\sqrt {x^{2}+1}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.286 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{1+2 y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.019 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (x^{2}+1\right )}{4 y^{3}} \\
y \left (0\right ) &= -\frac {\sqrt {2}}{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.143 |
|
| \begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.705 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.567 |
|
| \begin{align*}
\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
26.257 |
|
| \begin{align*}
\sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.185 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}+1}{-6 y+3 y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}}{-4+3 y^{2}} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.040 |
|
| \begin{align*}
y^{\prime }&=2 y^{2}+x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.149 |
|
| \begin{align*}
y^{\prime }&=\frac {2-{\mathrm e}^{x}}{3+2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.454 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \cos \left (2 x \right )}{3+2 y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.736 |
|
| \begin{align*}
y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.496 |
|
| \begin{align*}
y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.610 |
|
| \begin{align*}
y^{\prime }&=\frac {t y \left (4-y\right )}{1+t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.695 |
|
| \begin{align*}
y^{\prime }&=\frac {a y+b}{d +c y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.205 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.335 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+3 y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.232 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y-3 x}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.423 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x +3 y}{2 x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.745 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
10.463 |
|
| \begin{align*}
x^{2}+3 y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.144 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-3 y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.697 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y^{2}-x^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
66.503 |
|
| \begin{align*}
y \ln \left (t \right )+\left (t -3\right ) y^{\prime }&=2 t \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.476 |
|
| \begin{align*}
y+\left (t -4\right ) t y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.645 |
|
| \begin{align*}
\tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.258 |
|
| \begin{align*}
2 t y+\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (-3\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.658 |
|
| \begin{align*}
2 t y+\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.508 |
|
| \begin{align*}
y+\ln \left (t \right ) y^{\prime }&=\cot \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.337 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.018 |
|
| \begin{align*}
y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.432 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.253 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.256 |
|
| \begin{align*}
y^{3}+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.622 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.151 |
|
| \begin{align*}
y^{\prime }&=t \left (3-y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.551 |
|
| \begin{align*}
y^{\prime }&=y \left (3-t y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.311 |
|
| \begin{align*}
y^{\prime }&=-y \left (3-t y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.301 |
|
| \begin{align*}
y^{\prime }&=t -1-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
3.091 |
|
| \begin{align*}
y^{\prime }&=a y+b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.291 |
|
| \begin{align*}
y^{\prime }&=y \left (y-2\right ) \left (y-1\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.453 |
|
| \begin{align*}
y^{\prime }&=-1+{\mathrm e}^{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.395 |
|
| \begin{align*}
y^{\prime }&=-1+{\mathrm e}^{-y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.371 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 \arctan \left (y\right )}{1+y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.199 |
|
| \begin{align*}
y^{\prime }&=-k \left (y-1\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.388 |
|
| \begin{align*}
y^{\prime }&=y^{2} \left (y^{2}-1\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
y^{\prime }&=y \left (1-y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.094 |
|
| \begin{align*}
y^{\prime }&=-b \sqrt {y}+a y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.053 |
|
| \begin{align*}
y^{\prime }&=y^{2} \left (4-y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.887 |
|
| \begin{align*}
y^{\prime }&=\left (1-y\right )^{2} y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \begin{align*}
3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.988 |
|
| \begin{align*}
2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
19.358 |
|
| \begin{align*}
2+3 x^{2}-2 y x +\left (3-x^{2}+6 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.107 |
|
| \begin{align*}
2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
y^{\prime }&=\frac {-a x -b y}{b x +c y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.880 |
|
| \begin{align*}
y^{\prime }&=\frac {-a x +b y}{b x -c y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
12.389 |
|
| \begin{align*}
{\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 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
9.782 |
|
| \begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
✗ |
8.214 |
|