| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-a -y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.364 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x +y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.622 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x^{2}+y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.328 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+x^{2}+y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.329 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (x^{2}+1\right )-y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.998 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (3 x^{2}-y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.866 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.605 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=2 x \left (x -y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.327 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=2 x \left (x^{2}+1\right )^{2}+2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.263 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+\cos \left (x \right )&=2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.733 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\tan \left (x \right )-2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.834 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=a +4 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.417 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\left (2 b x +a \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.310 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=-1-y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.338 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.707 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=y^{2}-1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.687 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-y \left (2 x -y\right ) \\
\end{align*} | [_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] | ✓ | ✓ | ✓ | ✓ | 3.448 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=n \left (y^{2}-2 y x +1\right ) \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
1.357 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.642 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=x y \left (1+a y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.970 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+y^{2}-2 x y \left (1+y^{2}\right ) \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
60.670 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )&=x \left (x^{2}+1\right ) \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
11.938 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+x^{2}-y \,\operatorname {arccot}\left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.852 |
|
| \begin{align*}
\left (-x^{2}+4\right ) y^{\prime }+4 y&=\left (2+x \right ) y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.882 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=b +y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.331 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=\left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.093 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.830 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.897 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=a^{2}+3 y x -2 y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.750 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.030 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.551 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }&=a +\left (x +1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.530 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }&=2 y x +2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.372 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }&=2 y x -2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.358 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime }&=\left (1-2 x \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y&=a \\
\end{align*} | [_linear] | ✓ | ✓ | ✓ | ✓ | 3.297 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }&=a +2 \left (-x +2\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.586 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }+2-3 y x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.486 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime }&=\left (x +1\right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.270 |
|
| \begin{align*}
\left (x -2\right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.760 |
|
| \begin{align*}
x \left (x +a \right ) y^{\prime }&=\left (b +c y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.996 |
|
| \begin{align*}
\left (x +a \right )^{2} y^{\prime }&=2 \left (x +a \right ) \left (b +y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.385 |
|
| \begin{align*}
\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
16.660 |
|
| \begin{align*}
\left (x -a \right ) \left (-b +x \right ) y^{\prime }+k y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.441 |
|
| \begin{align*}
\left (x -a \right ) \left (-b +x \right ) y^{\prime }&=\left (x -a \right ) \left (-b +x \right )+\left (2 x -a -b \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.420 |
|
| \begin{align*}
\left (x -a \right ) \left (-b +x \right ) y^{\prime }&=c y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.620 |
|
| \begin{align*}
\left (x -a \right ) \left (-b +x \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.528 |
|
| \begin{align*}
\left (x -a \right ) \left (-b +x \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.143 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.947 |
|
| \begin{align*}
2 x^{2} y^{\prime }+x \cot \left (x \right )-1+2 x^{2} y \cot \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| \begin{align*}
2 x^{2} y^{\prime }+1+2 y x -y^{2} x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.902 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=2 y x +\left (-x \cot \left (x \right )+1\right ) \left (x^{2}-y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
99.829 |
|
| \begin{align*}
2 \left (-x^{2}+1\right ) y^{\prime }&=\sqrt {-x^{2}+1}+\left (x +1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.505 |
|
| \begin{align*}
x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| \begin{align*}
x \left (1-2 x \right ) y^{\prime }&=4 x -\left (4 x +1\right ) y+y^{2} \\
\end{align*} | [_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] | ✓ | ✓ | ✓ | ✓ | 5.013 |
|
| \begin{align*}
2 x \left (1-x \right ) y^{\prime }+x +\left (1-2 x \right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.579 |
|
| \begin{align*}
2 x \left (1-x \right ) y^{\prime }+x +\left (1-x \right ) y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.674 |
|
| \begin{align*}
2 \left (x^{2}+x +1\right ) y^{\prime }&=1+8 x^{2}-\left (2 x +1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.728 |
|
| \begin{align*}
4 \left (x^{2}+1\right ) y^{\prime }-4 y x -x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| \begin{align*}
a \,x^{2} y^{\prime }&=x^{2}+a x y+b^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
27.248 |
|
| \begin{align*}
\left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.829 |
|
| \begin{align*}
\left (b \,x^{2}+a \right ) y^{\prime }&=-A -B y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.665 |
|
| \begin{align*}
\left (b \,x^{2}+a \right ) y^{\prime }&=c x y \ln \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.068 |
|
| \begin{align*}
x \left (a x +1\right ) y^{\prime }+a -y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.984 |
|
| \begin{align*}
\left (b x +a \right )^{2} y^{\prime }+c y^{2}+\left (b x +a \right ) y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
16.308 |
|
| \begin{align*}
x^{3} y^{\prime }&=b \,x^{2} y+a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.973 |
|
| \begin{align*}
x^{3} y^{\prime }&=3-x^{2}+x^{2} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.583 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{4}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.078 |
|
| \begin{align*}
x^{3} y^{\prime }&=y \left (y+x^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.371 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (y-1\right ) x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.849 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (x +1\right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.045 |
|
| \begin{align*}
x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.879 |
|
| \begin{align*}
x^{3} y^{\prime }+3+\left (3-2 x \right ) x^{2} y-x^{6} y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.429 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (2 x^{2}+y^{2}\right ) y \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _Bernoulli] | ✓ | ✓ | ✓ | ✓ | 74.351 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{2}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.523 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{2}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.625 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{3}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.000 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=a -x^{2} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.538 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=\left (-x^{2}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.884 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=\left (x^{2}-x +1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.131 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{3}+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.111 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=x^{3} \left (-x^{2}+1\right )+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.720 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=2-4 x^{2} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.503 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=x -\left (5 x^{2}+3\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.588 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+x^{2}+\left (-x^{2}+1\right ) y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
177.820 |
|
| \begin{align*}
x^{2} \left (1-x \right ) y^{\prime }&=x \left (-x +2\right ) y-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.092 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (x^{2}-y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
41.958 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=\left (3 x^{2}+a y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.137 |
|
| \begin{align*}
6 x^{3} y^{\prime }&=4 x^{2} y+\left (1-3 x \right ) y^{4} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.124 |
|
| \begin{align*}
x \left (c \,x^{2}+b x +a \right ) y^{\prime }+x^{2}-\left (c \,x^{2}+b x +a \right ) y&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.891 |
|
| \begin{align*}
x^{4} y^{\prime }&=\left (x^{3}+y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.155 |
|
| \begin{align*}
x^{4} y^{\prime }+a^{2}+x^{4} y^{2}&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
7.272 |
|
| \begin{align*}
x^{4} y^{\prime }+x^{3} y+\csc \left (y x \right )&=0 \\
\end{align*} | [[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] | ✓ | ✓ | ✓ | ✗ | 3.554 |
|
| \begin{align*}
\left (-x^{4}+1\right ) y^{\prime }&=2 x \left (1-y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.471 |
|
| \begin{align*}
x \left (-x^{3}+1\right ) y^{\prime }&=2 x -\left (-4 x^{3}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| \begin{align*}
x \left (-x^{3}+1\right ) y^{\prime }&=x^{2}+\left (1-2 y x \right ) y \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.502 |
|
| \begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime }&=\left (x -3 x^{3} y\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.828 |
|
| \begin{align*}
x \left (-2 x^{3}+1\right ) y^{\prime }&=2 \left (-x^{3}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.273 |
|
| \begin{align*}
\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.424 |
|