| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
4 y^{\prime \prime }+x y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+y x&=2 \cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.645 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }-4 y&=6 \,{\mathrm e}^{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.595 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{1-x}+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{\left (-x^{2}+1\right )^{2}}+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.866 |
|
| \begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }+\left (x -2\right ) {\mathrm e}^{x} y^{\prime }+\frac {4 y}{x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.312 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.185 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-7 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.352 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x -y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.237 |
|
| \begin{align*}
4 x y^{\prime \prime }-x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.935 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+5 y \,{\mathrm e}^{2 x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.087 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+3 x y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| \begin{align*}
6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.195 |
|
| \begin{align*}
2 x y^{\prime \prime }+y^{\prime }-2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.872 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.078 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-\left (5+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.166 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+x \left (7+3 x \right ) y^{\prime }+\left (1+6 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.952 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.697 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+x \left (3 x^{2}+1\right ) y^{\prime }-2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.808 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.481 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (-x^{2}+x \right ) y^{\prime }+\left (x^{3}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.246 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (-2 x^{5}+9 x \right ) y^{\prime }+\left (10 x^{4}+5 x^{2}+25\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.924 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (4 x +\frac {1}{2} x^{2}-\frac {1}{3} x^{3}\right ) y^{\prime }-\frac {7 y}{4}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.174 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.976 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.867 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.881 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \cos \left (x \right ) y^{\prime }-2 y \,{\mathrm e}^{x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.632 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.052 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.255 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.721 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{3} y^{\prime }-\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.980 |
|
| \begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+7 \,{\mathrm e}^{x} y^{\prime } x +9 \left (1+\tan \left (x \right )\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.019 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.145 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
x y^{\prime \prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.730 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.168 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.879 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.063 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.727 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.652 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.050 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-\left (4 x +3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.296 |
|
| \begin{align*}
x y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.796 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.678 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
2.675 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-6 x y^{\prime }-4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| \begin{align*}
2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.119 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.984 |
|
| \begin{align*}
\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
4 x y^{\prime \prime }+3 y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\frac {3 x y^{\prime }}{2}-\frac {\left (x +1\right ) y}{2}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.967 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (2-x \right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.630 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.872 |
|
| \begin{align*}
y^{\prime \prime }+\left (1-\frac {3}{4 x^{2}}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.231 |
|
| \begin{align*}
5 y x +4 y^{2}+1+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
6.073 |
|
| \begin{align*}
2 x \tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.888 |
|
| \begin{align*}
y^{2} \left (x^{2}+1\right )+y+\left (1+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
13.098 |
|
| \begin{align*}
4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
41.040 |
|
| \begin{align*}
5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.175 |
|
| \begin{align*}
3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.212 |
|
| \begin{align*}
x -2 y-3+\left (2 x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.860 |
|
| \begin{align*}
6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }&=0 \\
y \left (\frac {1}{2}\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.695 |
|
| \begin{align*}
3 x -y-6+\left (x +y+2\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
57.316 |
|
| \begin{align*}
2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.522 |
|
| \begin{align*}
y&=y^{\prime }+\frac {{y^{\prime }}^{2}}{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.571 |
|
| \begin{align*}
\left (-x y^{\prime }+y\right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.681 |
|
| \begin{align*}
-x +y&={y^{\prime }}^{2} \left (1-\frac {2 y^{\prime }}{3}\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.177 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (-1+y\right ) x +\left (-1+y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.809 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
y^{\prime }&=1-x^{5}+\sqrt {x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \begin{align*}
3 y-2 x +\left (3 x -2\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.316 |
|
| \begin{align*}
x^{2}+x -1+\left (2 y x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.465 |
|
| \begin{align*}
{\mathrm e}^{2 y}+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.960 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-x^{2} y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.362 |
|
| \begin{align*}
y^{\prime }&=\frac {y-2 x}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.447 |
|
| \begin{align*}
x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.917 |
|
| \begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.526 |
|
| \begin{align*}
y^{\prime }+y&=x^{2}+2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.651 |
|