4.67 problem 64

Internal problem ID [6535]

Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 64.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {\frac {x y^{\prime \prime }}{-x^{2}+1}+y=0} \end {gather*}

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: 0.0 (sec). Leaf size: 0

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

Not solved