Internal problem ID [9572]
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]]
\[ \boxed {\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x=0} \]
✓ 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)
\[ y \left (x \right ) = c_{1} +\left (\frac {\ln \left (x -1\right )}{2}-\frac {\ln \left (x +1\right )}{2}\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 27
DSolve[2*x*y'[x] + (-1 + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} c_1 (\log (1-x)-\log (x+1))+c_2 \]