| # |
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]‘]] |
✓ |
✓ |
✗ |
✗ |
9.896 |
|
| \begin{align*}
2 y^{\prime } x -y&=y^{\prime } \ln \left (y^{\prime } y\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
42.170 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y x +x^{3} y^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
2.568 |
|
| \begin{align*}
y^{\prime }&=a x +b \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
8.402 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=1+y+\left (x +1\right ) \sqrt {1+y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
46.320 |
|
| \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]‘]] |
✓ |
✓ |
✓ |
✓ |
2.326 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
4.911 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✗ |
✓ |
✗ |
164.372 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-1-y&=\left (x +1\right ) \sqrt {1+y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
41.116 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.634 |
|
| \begin{align*}
y^{\prime }-a \sqrt {y}-b x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
8.155 |
|
| \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]‘]] |
✓ |
✓ |
✓ |
✓ |
3.050 |
|
| \begin{align*}
\left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+y^{5}+y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
6.665 |
|
| \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] |
✓ |
✗ |
✓ |
✗ |
209.451 |
|
| \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]‘]] |
✓ |
✓ |
✓ |
✓ |
5.548 |
|
| \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’)‘] |
✓ |
✓ |
✓ |
✗ |
14.767 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
11.144 |
|
| \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] | ✓ | ✓ | ✓ | ✗ | 13.635 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
12.937 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
48.167 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
48.372 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
10.876 |
|
| \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] |
✓ |
✗ |
✓ |
✗ |
18.220 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
12.977 |
|
| \begin{align*}
y^{\prime }&=-\frac {1296 y}{216-648 x^{2} y+216 x^{2}-432 y x -882 y^{6}-216 x^{2} y^{4}-1296 y+216 x y^{2}-1944 y^{4}+1080 x y^{3}-570 y^{8}-648 y^{2} x^{2}+216 y^{7} x -1728 y^{3}+72 y^{8} x +216 x^{3}-2376 y^{2}-612 y^{5}-324 x^{2} y^{3}+594 x y^{6}+1080 x y^{5}+1152 y^{4} x -846 y^{7}-126 y^{10}-8 y^{12}-36 y^{11}-315 y^{9}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
12.604 |
|
| \begin{align*}
y^{\prime }&=-\frac {216 y \left (-2 y^{4}-3 y^{3}-6 y^{2}-6 y+6 x +6\right )}{-648 x^{2} y-1296 y x +2484 y^{6}-216 x^{2} y^{4}-1296 y-1944 x y^{2}+2808 y^{4}-648 x y^{3}-18 y^{8}-648 y^{2} x^{2}+216 y^{7} x +1728 y^{3}+72 y^{8} x +216 x^{3}-1296 y^{2}+4428 y^{5}-324 x^{2} y^{3}+594 x y^{6}+1080 x y^{5}-432 y^{4} x +594 y^{7}-126 y^{10}-8 y^{12}-36 y^{11}-315 y^{9}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
23.492 |
|
| \begin{align*}
y^{\prime }-\frac {1+y}{x +1}&=\sqrt {1+y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
45.606 |
|
| \begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
1.659 |
|
| \begin{align*}
y^{\prime } y+1&=\left (x -1\right ) {\mathrm e}^{-\frac {y^{2}}{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
6.957 |
|
| \begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
1.475 |
|
| \begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
5.847 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
42.804 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
43.510 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2} y^{3}+y x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
12.730 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y^{2}+x^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
1.926 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y^{2}+x^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
58.167 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}-y^{2}} \\
y \left (1\right ) &= 2 \\
\end{align*} | [‘y=_G(x,y’)‘] | ✓ | ✓ | ✗ | ✗ | 1.347 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}+4 y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
0.804 |
|
| \begin{align*}
y^{4}+\left (x^{2}-3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
✗ |
2.189 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
6.366 |
|
| \begin{align*}
\sin \left (y\right ) \left (x +\sin \left (y\right )\right )+2 x^{2} y^{\prime } \cos \left (y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
50.772 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
53.100 |
|