| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
1+x y \left (x y^{2}+1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✗ |
✗ |
3.556 |
|
| \begin{align*}
x&=y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.626 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y x +x^{3} y^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.036 |
|
| \begin{align*}
y^{\prime }+x \left (\sin \left (2 y\right )-x^{2} \cos \left (y\right )^{2}\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
17.252 |
|
| \begin{align*}
x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime }&=6 y^{3} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
8.241 |
|
| \begin{align*}
\left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+\left (1+y^{4}\right ) y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
7.650 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
252.651 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✗ |
1444.556 |
|
| \begin{align*}
2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 y x \right ) y y^{\prime }+2 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
346.477 |
|
| \begin{align*}
x -2 \sin \left (y\right )+3+\left (2 x -4 \sin \left (y\right )-3\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
20.757 |
|
| \begin{align*}
\left (\frac {y^{2}}{b}+\frac {x^{2}}{a}\right ) \left (x +y y^{\prime }\right )+\frac {\left (a -b \right ) \left (y y^{\prime }-x \right )}{a +b}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
21.279 |
|
| \begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }-1&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
2.943 |
|
| \begin{align*}
\left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+y^{5}+y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
4.546 |
|
| \begin{align*}
a x y {y^{\prime }}^{2}-\left (a y^{2}+b \,x^{2}+c \right ) y^{\prime }+b x y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
192.034 |
|
| \begin{align*}
2 \left (y^{\prime } x +y\right )^{3}-y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
306.769 |
|
| \begin{align*}
{y^{\prime }}^{n}-f \left (x \right ) g \left (y\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.770 |
|
| \begin{align*}
y^{\prime }&=-\frac {\left (a \,x^{2}-2 F \left (y+\frac {a \,x^{4}}{8}\right )\right ) x}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
9.563 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (\frac {y}{\sqrt {x^{2}+1}}\right ) x}{\sqrt {x^{2}+1}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
13.619 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{2} \left (a x -2 \sqrt {a \left (a \,x^{4}+8 y\right )}\right )}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
68.730 |
|
| \begin{align*}
y^{\prime }&=\frac {i x \left (i-2 \sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y\right )}\right ) y}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
31.982 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x \left (x y^{2}+1+x \right ) y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.242 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (2 x +2+y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
✗ |
11.134 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
5.694 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+3 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+9 y} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
79.120 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x +y+1\right ) y}{\left (x +y+2 y^{3}\right ) \left (x +1\right )} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
9.837 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (3+y\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{243 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+243 y} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
89.007 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (\left (x^{2}+1\right )^{{3}/{2}} x^{2}+\left (x^{2}+1\right )^{{3}/{2}}+y^{2} \left (x^{2}+1\right )^{{3}/{2}}+x^{2} y^{3}+y^{3}\right ) x}{\left (x^{2}+1\right )^{3}} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
70.347 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x +y+1\right ) y}{\left (y^{4}+y^{3}+y^{2}+x \right ) \left (x +1\right )} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
10.237 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (x -y\right ) \left (1+y\right )}{x \left (y x +x -y\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
27.123 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (x +y\right ) \left (1+y\right )}{x \left (y x +x +y\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
26.207 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{8}}{y^{5}+2 y^{6}+2 y^{2}+16 y^{4} x +32 y^{6} x^{2}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
6.589 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{6} \left (1+4 x y^{2}+y^{2}\right )}{y^{3}+4 x y^{5}+y^{5}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \\
\end{align*} |
[_rational] |
✓ |
✗ |
✓ |
✗ |
18.177 |
|
| \begin{align*}
y^{\prime }&=-\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 y x +60 y^{5}-36 x y^{3}-72 x y^{2}-24 y^{4} x +4 y^{8}+12 y^{7}+33 y^{6}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
7.743 |
|
| \begin{align*}
y^{\prime }&=-\frac {1296 y}{216-1296 y+216 x^{2}-432 y x +216 x^{3}+1080 x y^{5}-570 y^{8}-315 y^{9}-882 y^{6}-2376 y^{2}+1080 x y^{3}-1728 y^{3}-324 x^{2} y^{3}+72 y^{8} x +216 y^{7} x +1152 y^{4} x -216 x^{2} y^{4}-1944 y^{4}-126 y^{10}-8 y^{12}-36 y^{11}-846 y^{7}-612 y^{5}-648 y^{2} x^{2}+216 x y^{2}-648 x^{2} y+594 x y^{6}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
8.525 |
|
| \begin{align*}
y^{\prime }&=-\frac {216 y \left (-2 y^{4}-3 y^{3}-6 y^{2}-6 y+6 x +6\right )}{-1296 y-1296 y x +216 x^{3}+1080 x y^{5}-18 y^{8}-315 y^{9}+2484 y^{6}-1296 y^{2}-648 x y^{3}+1728 y^{3}-324 x^{2} y^{3}+72 y^{8} x +216 y^{7} x -432 y^{4} x -216 x^{2} y^{4}+2808 y^{4}-126 y^{10}-8 y^{12}-36 y^{11}+594 y^{7}+4428 y^{5}-648 y^{2} x^{2}-1944 x y^{2}-648 x^{2} y+594 x y^{6}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
14.376 |
|
| \begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
8.405 |
|
| \begin{align*}
y^{\prime } x&=\arcsin \left (x^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.585 |
|
| \begin{align*}
{\mathrm e}^{y}-2 t y+\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✗ |
✗ |
6.704 |
|
| \begin{align*}
y y^{\prime }+1&=\left (-1+x \right ) {\mathrm e}^{-\frac {y^{2}}{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
8.824 |
|
| \begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.968 |
|
| \begin{align*}
{y^{\prime }}^{3}-x^{3} \left (1-y^{\prime }\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
48.233 |
|
| \begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
6.411 |
|
| \begin{align*}
y^{\prime }+\frac {\tan \left (y\right )}{x}&=\frac {\tan \left (y\right ) \sin \left (y\right )}{x^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
52.243 |
|
| \begin{align*}
y^{\prime }+\frac {\tan \left (y\right )}{x}&=\frac {\tan \left (y\right ) \sin \left (y\right )}{x^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
51.964 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}-1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
289.888 |
|
| \begin{align*}
y^{\prime }+x \sin \left (2 y\right )&=x^{3} \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
31.300 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2} y^{3}+y x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
9.372 |
|
| \begin{align*}
y^{3} \left (x +y y^{\prime }\right )&=\left (x^{2}+y^{2}\right )^{3} y^{\prime } \\
\end{align*} |
[_rational] |
✓ |
✗ |
✗ |
✗ |
45.909 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}+y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
11.496 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}+y^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
7.605 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}-y^{2}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
14.316 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}+4 y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
12.457 |
|
| \begin{align*}
x^{3}+2 x y^{2}-x +\left (x^{2} y+2 y^{3}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
82.756 |
|
| \begin{align*}
y^{4}+\left (x^{2}-3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
✗ |
17.940 |
|
| \begin{align*}
x \left (\left (x^{2}+y^{2}\right )^{{3}/{2}}+2 y^{2}\right )+y \left (\left (x^{2}+y^{2}\right )^{{3}/{2}}-2 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
252.559 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{5}+y x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
96.440 |
|
| \begin{align*}
\sin \left (y\right ) \left (x +\sin \left (y\right )\right )+2 x^{2} \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
98.533 |
|
| \begin{align*}
3 \sin \left (y\right )-5 x +2 x^{2} \cot \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
49.456 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) x&=\cot \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.425 |
|
| \begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
27.658 |
|
| \begin{align*}
x^{3} y^{\prime }-\cos \left (y\right )&=1 \\
y \left (\infty \right ) &= 5 \pi \\
\end{align*} |
[_separable] |
✓ |
✗ |
✗ |
✗ |
10.692 |
|
| \begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
32.635 |
|
| \begin{align*}
y^{\prime }+\sin \left (y\right )+x \cos \left (y\right )+x&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
51.526 |
|
| \begin{align*}
x&=y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
73.030 |
|
| \begin{align*}
y^{\prime }+\tan \left (y\right )&=x \sec \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
84.556 |
|
| \begin{align*}
{y^{\prime }}^{4}&=4 y \left (y^{\prime } x -2 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
1371.358 |
|
| \begin{align*}
\tan \left (y\right ) y^{\prime }+4 \cos \left (y\right ) x^{3}&=2 x \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
218.609 |
|
| \begin{align*}
\tan \left (y\right ) y^{\prime }+4 \cos \left (y\right ) x^{3}&=2 x \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
197.723 |
|