Internal problem ID [7827]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 342.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
\[ \boxed {\left (1-x^{2}\right ) y^{\prime \prime }-2 x y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve((1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x +c_{2} \left (-\frac {\ln \left (x +1\right ) x}{2}+\frac {\ln \left (x -1\right ) x}{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 33
DSolve[(1-x^2)*y''[x]-2*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x-\frac {1}{2} c_2 (x \log (1-x)-x \log (x+1)+2) \]