| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=y-x^{2}+2 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.625 |
|
| \begin{align*}
y^{\prime }&=\frac {x -1}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.818 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.476 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.176 |
|
| \begin{align*}
y^{\prime }&=\frac {y x}{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.361 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
13.906 |
|
| \begin{align*}
y^{\prime }&=1+x y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
20.814 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +1}-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.334 |
|
| \begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.138 |
|
| \begin{align*}
y y^{\prime } x +1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.196 |
|
| \begin{align*}
\left (y^{2}+x y^{2}\right ) y^{\prime }+x^{2}-x^{2} y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| \begin{align*}
1+y^{2}&=y^{\prime } x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.292 |
|
| \begin{align*}
y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.985 |
|
| \begin{align*}
x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.155 |
|
| \begin{align*}
{\mathrm e}^{-y} \left (1+y^{\prime }\right )&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.280 |
|
| \begin{align*}
y \ln \left (y\right )+y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.424 |
|
| \begin{align*}
y^{\prime }&=a^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.793 |
|
| \begin{align*}
{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.657 |
|
| \begin{align*}
\left ({\mathrm e}^{x}+1\right ) y y^{\prime }&={\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.149 |
|
| \begin{align*}
\left (1+y^{2}\right ) {\mathrm e}^{2 x}-\left (1+y^{2}\right ) {\mathrm e}^{y} y^{\prime }-\left (1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.407 |
|
| \begin{align*}
x y^{2}-y^{2}+x -1+\left (x^{2} y-2 y x +x^{2}+2 y-2 x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.824 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.463 |
|
| \begin{align*}
y^{\prime }&=a x +b y+c \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.902 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
88.289 |
|
| \begin{align*}
x -y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.766 |
|
| \begin{align*}
1+y^{2}&=\left (y-\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.077 |
|
| \begin{align*}
x y^{2} \left (y^{\prime } x +y\right )&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.415 |
|
| \begin{align*}
y^{2} x^{2}+1+2 x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
2.242 |
|
| \begin{align*}
\left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \begin{align*}
x^{2} y^{3}+y+x -2+\left (x +x^{3} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.213 |
|
| \begin{align*}
x^{6}-2 x^{5}+2 x^{4}-y^{3}+4 x^{2} y+\left (x y^{2}-4 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
✓ |
✓ |
✗ |
3.645 |
|
| \begin{align*}
1+y^{\prime }&=\frac {\left (x +y\right )^{m}}{\left (x +y\right )^{n}+\left (x +y\right )^{p}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.785 |
|
| \begin{align*}
\ln \left (x \right )+y^{3}-3 y^{2} y^{\prime } x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.040 |
|
| \begin{align*}
y x +2 x y \ln \left (y\right )^{2}+y \ln \left (y\right )+\left (2 x^{2} \ln \left (y\right )+x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.910 |
|
| \begin{align*}
-y^{\prime } x +y&=a \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.940 |
|
| \begin{align*}
a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }&=0 \\
y \left (a \right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.299 |
|
| \begin{align*}
y^{\prime }+\sin \left (\frac {x}{2}+\frac {y}{2}\right )&=\sin \left (\frac {x}{2}-\frac {y}{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.956 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.450 |
|
| \begin{align*}
y^{\prime }&=y^{a} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
5.721 |
|
| \begin{align*}
y^{\prime }&=y \ln \left (y\right )^{a} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✗ |
✗ |
✗ |
✗ |
16.808 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) y&=x \tan \left (x \right )+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.839 |
|
| \begin{align*}
\cos \left (y^{\prime }\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| \begin{align*}
{\mathrm e}^{y^{\prime }}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
\sin \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
\tan \left (y^{\prime }\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.499 |
|
| \begin{align*}
{\mathrm e}^{y^{\prime }}&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \begin{align*}
\tan \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.334 |
|
| \begin{align*}
x^{2} y^{\prime } \cos \left (y\right )+1&=0 \\
y \left (\infty \right ) &= 2 \pi \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
8.378 |
|
| \begin{align*}
x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {5 \pi }{4} \\
\end{align*} |
[_separable] |
✗ |
✓ |
✗ |
✗ |
9.183 |
|
| \begin{align*}
x^{3} y^{\prime }-\cos \left (y\right )&=1 \\
y \left (\infty \right ) &= 5 \pi \\
\end{align*} |
[_separable] |
✓ |
✗ |
✗ |
✗ |
9.613 |
|
| \begin{align*}
2 \left (x^{2}+1\right ) y^{\prime }-\cos \left (2 y\right )^{2}&=0 \\
y \left (-\infty \right ) &= \frac {7 \pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
7.180 |
|
| \begin{align*}
{\mathrm e}^{y}&={\mathrm e}^{4 y} y^{\prime }+1 \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
4.047 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=-1+y \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✗ |
✓ |
✗ |
✓ |
6.156 |
|
| \begin{align*}
y^{\prime }&=2 x \left (\pi +y\right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✗ |
✓ |
✗ |
✓ |
7.970 |
|
| \begin{align*}
x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {11 \pi }{4} \\
\end{align*} |
[_separable] |
✗ |
✓ |
✗ |
✓ |
20.300 |
|
| \begin{align*}
4 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.442 |
|