Internal problem ID [1747]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
\[ \boxed {\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (t \right ) = t c_{1} +c_{2} \left (-\frac {\ln \left (t +1\right ) t}{2}+\frac {\ln \left (t -1\right ) t}{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (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_2 (t \text {arctanh}(t)-1)+c_1 t \\ \end{align*}