| # |
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] |
✓ |
✓ |
✓ |
✓ |
1.909 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x +y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.749 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-x^{2}+y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.844 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+x^{2}+y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.822 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (x^{2}+1\right )-y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.394 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (3 x^{2}-y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.241 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.890 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=2 x \left (x -y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.909 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=2 x \left (x^{2}+1\right )^{2}+2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.064 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+\cos \left (x \right )&=2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.303 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\tan \left (x \right )-2 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.432 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=a +4 y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.040 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\left (2 b x +a \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.413 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.857 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=-1-y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.785 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.508 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=-1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.470 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
3.917 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=n \left (1-2 y x +y^{2}\right ) \\
\end{align*} |
[_rational, _Riccati] |
✗ |
✓ |
✓ |
✗ |
1.845 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.575 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=x y \left (1+a y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.842 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+y^{2}-2 x y \left (1+y^{2}\right ) \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
132.893 |
|
| \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’)‘] |
✗ |
✓ |
✓ |
✗ |
10.467 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+x^{2}-y \,\operatorname {arccot}\left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.777 |
|
| \begin{align*}
\left (-x^{2}+4\right ) y^{\prime }+4 y&=\left (2+x \right ) y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.890 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=b +y x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.170 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
8.126 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.819 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.761 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=a^{2}+3 y x -2 y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.095 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.512 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.670 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }&=a +\left (x +1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.207 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }&=2 y x +2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.926 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }&=2 y x -2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.903 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime }&=\left (1-2 x \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.083 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y&=a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.323 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }&=a +2 \left (-x +2\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.719 |
|
| \begin{align*}
x \left (1-x \right ) y^{\prime }+2-3 y x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.046 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
3.373 |
|
| \begin{align*}
\left (x -2\right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 y x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.368 |
|
| \begin{align*}
x \left (a +x \right ) y^{\prime }&=\left (b +c y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.874 |
|
| \begin{align*}
\left (a +x \right )^{2} y^{\prime }&=2 \left (a +x \right ) \left (b +y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.360 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
18.049 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }+k y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.946 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }&=\left (x -a \right ) \left (x -b \right )+\left (2 x -a -b \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.808 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }&=c y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.589 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.889 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \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] |
✓ |
✓ |
✓ |
✓ |
11.268 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.444 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
3.063 |
|
| \begin{align*}
2 x^{2} y^{\prime }+1+2 y x -y^{2} x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.361 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
82.721 |
|
| \begin{align*}
2 \left (-x^{2}+1\right ) y^{\prime }&=\sqrt {-x^{2}+1}+\left (x +1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.901 |
|
| \begin{align*}
x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.010 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
6.446 |
|
| \begin{align*}
2 x \left (1-x \right ) y^{\prime }+x +\left (1-2 x \right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.176 |
|
| \begin{align*}
2 x \left (1-x \right ) y^{\prime }+x +\left (1-x \right ) y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.026 |
|
| \begin{align*}
2 \left (x^{2}+x +1\right ) y^{\prime }&=1+8 x^{2}-\left (2 x +1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.468 |
|
| \begin{align*}
4 \left (x^{2}+1\right ) y^{\prime }-4 y x -x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.134 |
|
| \begin{align*}
a \,x^{2} y^{\prime }&=x^{2}+a x y+b^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
30.750 |
|
| \begin{align*}
\left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.001 |
|
| \begin{align*}
\left (b \,x^{2}+a \right ) y^{\prime }&=-A -B y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.620 |
|
| \begin{align*}
\left (b \,x^{2}+a \right ) y^{\prime }&=c x y \ln \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.943 |
|
| \begin{align*}
x \left (a x +1\right ) y^{\prime }+a -y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.579 |
|
| \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] |
✗ |
✓ |
✓ |
✗ |
19.181 |
|
| \begin{align*}
x^{3} y^{\prime }&=b \,x^{2} y+a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.660 |
|
| \begin{align*}
x^{3} y^{\prime }&=3-x^{2}+x^{2} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.567 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{4}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.735 |
|
| \begin{align*}
x^{3} y^{\prime }&=y \left (y+x^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.924 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (-1+y\right ) x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.395 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (x +1\right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.388 |
|
| \begin{align*}
x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.879 |
|
| \begin{align*}
x^{3} y^{\prime }+3+\left (3-2 x \right ) x^{2} y-x^{6} y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (2 x^{2}+y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
147.148 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{2}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.102 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{2}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.176 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{3}+y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.114 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=a -x^{2} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.026 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=\left (-x^{2}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.807 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=\left (x^{2}-x +1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.174 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{3}+\left (-2 x^{2}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.011 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
4.286 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=2-4 x^{2} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.000 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }&=x -\left (5 x^{2}+3\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.107 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+x^{2}+y^{2} \left (-x^{2}+1\right )&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
94.371 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
5.996 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (x^{2}-y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
82.931 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=\left (3 x^{2}+a y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.028 |
|
| \begin{align*}
6 x^{3} y^{\prime }&=4 x^{2} y+\left (1-3 x \right ) y^{4} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.027 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
6.067 |
|
| \begin{align*}
x^{4} y^{\prime }&=\left (x^{3}+y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.760 |
|
| \begin{align*}
x^{4} y^{\prime }+a^{2}+y^{2} x^{4}&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
8.340 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.664 |
|
| \begin{align*}
\left (-x^{4}+1\right ) y^{\prime }&=2 x \left (1-y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.325 |
|
| \begin{align*}
x \left (-x^{3}+1\right ) y^{\prime }&=2 x -\left (-4 x^{3}+1\right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.296 |
|
| \begin{align*}
x \left (-x^{3}+1\right ) y^{\prime }&=x^{2}+\left (1-2 y x \right ) y \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.662 |
|
| \begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime }&=\left (x -3 x^{3} y\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| \begin{align*}
x \left (-2 x^{3}+1\right ) y^{\prime }&=2 \left (-x^{3}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.490 |
|
| \begin{align*}
\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.684 |
|