Internal problem ID [6787]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 55.
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 }-8 x y^{\prime }-12 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve((1-x^2)*diff(y(x),x$2)-8*x*diff(y(x),x)-12*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (3 x^{2}+1\right )}{\left (x^{2}-1\right )^{3}}+\frac {c_{2} \left (x^{3}+3 x \right )}{\left (x^{2}-1\right )^{3}} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 37
DSolve[(1-x^2)*y''[x]-8*x*y'[x]-12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 c_1 (x-1)^3-c_2 \left (3 x^2+1\right )}{3 \left (x^2-1\right )^3} \\ \end{align*}