Internal problem ID [6928]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 196.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
Solve \begin {gather*} \boxed {\left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve((1-t^2)*diff(y(t),t$2)-2*t*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} t +c_{2} \left (\frac {\ln \left (t -1\right ) t}{2}-\frac {\ln \left (t +1\right ) t}{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 19
DSolve[(1-t^2)*y''[t]-2*t*y'[t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 t+c_2 \left (t \tanh ^{-1}(t)-1\right ) \\ \end{align*}