Internal problem ID [8817]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1237.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve((x^2-1)*diff(diff(y(x),x),x)+2*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+\left (\frac {\ln \left (x -1\right )}{2}-\frac {\ln \left (x +1\right )}{2}\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 14
DSolve[2*x*y'[x] + (-1 + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-c_1 \tanh ^{-1}(x) \\ \end{align*}