| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (a -3 x^{2}-y^{2}\right ) y y^{\prime }+x \left (a -x^{2}+y^{2}\right )&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
96.299 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
195.393 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
174.573 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-a^{2}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.841 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+a -x^{2}+2 y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.600 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +a \,x^{2}+\left (1-a \right ) y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.895 |
|
| \begin{align*}
2 y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-1+x^{2}+y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.677 |
|
| \begin{align*}
\left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.616 |
|
| \begin{align*}
9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
158.332 |
|
| \begin{align*}
y^{3} {y^{\prime }}^{3}-\left (-3 x +1\right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
3.821 |
|
| \begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=R^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.944 |
|
| \begin{align*}
4 x^{2} y y^{\prime }&=3 x \left (3 y^{2}+2\right )+2 \left (3 y^{2}+2\right )^{3} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✓ |
19.938 |
|
| \begin{align*}
1+{y^{\prime }}^{2}&=\frac {1}{y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-a^{2}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.574 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+a y^{2}+b x +c&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
30.790 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+a -x^{2}+2 y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.637 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +a \,x^{2}+\left (1-a \right ) y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.727 |
|
| \begin{align*}
\left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.866 |
|
| \begin{align*}
9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
64.535 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (\frac {a y^{2}+b \,x^{2}}{a}\right ) x}{\sqrt {a}\, y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
12.555 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (-\frac {-y^{2}+b}{x^{2}}\right ) x}{y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
9.171 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (\frac {1+x y^{2}}{x}\right )}{y x^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
7.691 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-y^{2}+4 a x \right )^{2}}{y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✓ |
6.803 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (a y^{2}+b \,x^{2}\right )^{2} x}{a^{{5}/{2}} y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
19.907 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a +x \sqrt {-y^{2}+4 a x}}{y} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
21.138 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a +x^{2} \sqrt {-y^{2}+4 a x}}{y} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
20.972 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+x y^{2}\right )^{2}}{y x^{4}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
7.942 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-y^{2}+4 a x \right )^{3}}{\left (-y^{2}+4 a x -1\right ) y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
10.945 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (a y^{2}+b \,x^{2}\right )^{3} x}{a^{{5}/{2}} \left (a y^{2}+b \,x^{2}+a \right ) y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
16.582 |
|
| \begin{align*}
y^{\prime }&=-\frac {i \left (8 i x +16 y^{4}+8 x^{2} y^{2}+x^{4}\right )}{32 y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.881 |
|
| \begin{align*}
y^{\prime }&=-\frac {i \left (i x +x^{4}+2 x^{2} y^{2}+y^{4}\right )}{y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
5.479 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x -y\right )^{2} \left (x +y\right )^{2} x}{y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
10.494 |
|
| \begin{align*}
y^{\prime }&=-\frac {i \left (54 i x^{2}+81 y^{4}+18 y^{2} x^{4}+x^{8}\right ) x}{243 y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
7.391 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+x y^{2}\right )^{3}}{x^{4} \left (x y^{2}+1+x \right ) y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
10.099 |
|
| \begin{align*}
y^{\prime }&=-\frac {i \left (16 i x^{2}+16 y^{4}+8 y^{2} x^{4}+x^{8}\right ) x}{32 y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
7.071 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x -y\right )^{3} \left (x +y\right )^{3} x}{\left (x^{2}-y^{2}-1\right ) y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
12.682 |
|
| \begin{align*}
y^{\prime }&=\frac {b \,x^{3}+c^{2} \sqrt {a}-2 c b \,x^{2} \sqrt {a}+2 c y^{2} a^{{3}/{2}}+b^{2} x^{4} \sqrt {a}-2 y^{2} a^{{3}/{2}} b \,x^{2}+a^{{5}/{2}} y^{4}}{a \,x^{2} y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
13.008 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{4}-8 a x y^{2}+16 a^{2} x^{2}+y^{6}-12 y^{4} a x +48 y^{2} a^{2} x^{2}-64 a^{3} x^{3}}{y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
11.704 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (a^{3}+y^{4} a^{3}+2 a^{2} y^{2} b \,x^{2}+b^{2} x^{4} a +y^{6} a^{3}+3 y^{4} a^{2} b \,x^{2}+3 y^{2} a \,b^{2} x^{4}+b^{3} x^{6}\right ) x}{a^{{7}/{2}} y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
18.221 |
|
| \begin{align*}
y^{\prime }&=-\frac {\left (-1-y^{4}+2 x^{2} y^{2}-x^{4}-y^{6}+3 x^{2} y^{4}-3 y^{2} x^{4}+x^{6}\right ) x}{y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
14.095 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+x^{3} y^{4}+2 x^{2} y^{2}+x +x^{3} y^{6}+3 x^{2} y^{4}+3 x y^{2}+1}{x^{5} y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
10.502 |
|
| \begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=a^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.449 |
|
| \begin{align*}
\left (x y^{\prime }-y\right ) \left (y y^{\prime }+x \right )&=a^{2} y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
135.917 |
|
| \begin{align*}
x y \left (1-{y^{\prime }}^{2}\right )&=\left (-y^{2}-a^{2}+x^{2}\right ) y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
158.413 |
|
| \begin{align*}
y y^{\prime }+y^{4}&=\sin \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
13.519 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| \begin{align*}
y^{\prime } \left (x^{2}+y^{2}+3\right )&=2 x \left (2 y-\frac {x^{2}}{y}\right ) \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
53.610 |
|
| \begin{align*}
y^{2} \left (1-{y^{\prime }}^{2}\right )&=b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
\left (x y^{\prime }-y\right ) \left (y y^{\prime }+x \right )&=h^{2} y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
60.777 |
|
| \begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=r^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
\left (x y^{\prime }-y\right ) \left (x -y y^{\prime }\right )&=2 y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
56.595 |
|
| \begin{align*}
\left (a {y^{\prime }}^{2}-b \right ) x y+\left (b \,x^{2}-a y^{2}+c \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
101.198 |
|
| \begin{align*}
\left (x y^{\prime }-y\right ) \left (y y^{\prime }+x \right )&=h^{2} y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
75.246 |
|
| \begin{align*}
a x y {y^{\prime }}^{2}+\left (x^{2}-a y^{2}-b \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
108.727 |
|
| \begin{align*}
\left (x y^{\prime }-y\right ) \left (x -y y^{\prime }\right )&=2 y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
65.365 |
|
| \begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=r^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-a^{2}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| \begin{align*}
1+{y^{\prime }}^{2}&=\frac {1}{y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.661 |
|
| \begin{align*}
a x y {y^{\prime }}^{2}+\left (x^{2}-a y^{2}-b \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
101.651 |
|
| \begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y y^{\prime }+x&=\frac {\left (x^{2}+y^{2}\right )^{2}}{2 x^{2}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
6.794 |
|