Internal problem ID [7135]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 411.
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 }-6 x y^{\prime }+12 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 24
dsolve((x^2-1)*diff(y(x),x$2)-6*x*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x^{3}+x \right )+c_{2} \left (x^{4}+6 x^{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 45
DSolve[(x^2-1)*y''[x]-6*x*y'[x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x^2-1} \left (c_2 x \left (x^2+1\right )+c_1 (x-1)^4\right )}{\sqrt {1-x^2}} \\ \end{align*}