Internal problem ID [7522]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 805.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 51
dsolve(x^2*(1-x^2)*diff(y(x),x$2)+2*x*(1-x^2)*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x^{2}-1\right )}{x^{2}}+\frac {c_{2} \left (\ln \left (x -1\right ) x^{2}-\ln \left (x +1\right ) x^{2}-\ln \left (x -1\right )+\ln \left (x +1\right )-2 x \right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 35
DSolve[x^2*(1-x^2)*y''[x]+2*x*(1-x^2)*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 \left (\left (x^2-1\right ) \tanh ^{-1}(x)+x\right )-2 c_1 \left (x^2-1\right )}{2 x^2} \\ \end{align*}