| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
a \left (1+k \right ) x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
11.514 |
|
| \begin{align*}
\left (\cos \left (x \right )^{2} a -\sec \left (x \right )^{2}\right ) y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.901 |
|
| \begin{align*}
\frac {x y^{\prime \prime }}{1-x}+y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
a x y^{\prime \prime }+\left (b x +3 a \right ) y^{\prime }+3 b y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.056 |
|
| \begin{align*}
y^{\prime \prime }&=-\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (-17 \sin \left (x \right )^{2}-1\right ) y}{4 \sin \left (x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.295 |
|
| \begin{align*}
y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a \left (n +1\right ) x^{n -1}+b \left (m +1\right ) x^{m -1}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
6.832 |
|
| \begin{align*}
x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+a \left (b +n -1\right ) x^{n -1} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.326 |
|
| \begin{align*}
\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) \left (c \,x^{2}+d \right ) y^{\prime }+2 \left (-a d +b c \right ) x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
6.949 |
|
| \begin{align*}
\left (a \,x^{n}+b \right )^{m +1} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }-a n m \,x^{n -1} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.351 |
|
| \begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+y&=1 \\
y \left (\infty \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
22.739 |
|
| \begin{align*}
x u^{\prime \prime }-\left ({\mathrm e}^{x} x^{2}+1\right ) u^{\prime }-x^{2} {\mathrm e}^{x} u&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✗ |
✗ |
1.773 |
|
| \begin{align*}
x^{2} \ln \left (x \right )^{2} y^{\prime \prime }-x \ln \left (x \right ) y^{\prime }+\left (1+\ln \left (x \right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.808 |
|
| \begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+y&=1 \\
y \left (\infty \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.209 |
|