56.4.67 problem 64

Internal problem ID [8956]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 64
Date solved : Monday, January 27, 2025 at 05:20:50 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \frac {x y^{\prime \prime }}{-x^{2}+1}+y&=0 \end{align*}

✗ Solution by Maple

dsolve(x/(1-x^2)*diff(y(x),x$2)+y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[x/(1-x^2)*D[y[x],{x,2}]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved