Internal problem ID [6735]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 1.
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: 0.0 (sec). Leaf size: 15
dsolve((x^2-1)*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} \left (x^{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 39
DSolve[(x^2-1)*y''[x]-2*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {x^2-1} \left (c_1 (x-1)^2+c_2 x\right )}{\sqrt {1-x^2}} \\ \end{align*}