Internal problem ID [7133]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 409.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
Solve \begin {gather*} \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 26
dsolve((1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} \left (\frac {\ln \left (x -1\right ) x}{2}-\frac {\ln \left (x +1\right ) x}{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 19
DSolve[(1-x^2)*y''[x]-2*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x+c_2 \left (x \tanh ^{-1}(x)-1\right ) \\ \end{align*}