56.4.67 problem 64

Internal problem ID [8956]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 64
Date solved : Sunday, March 30, 2025 at 01:56:25 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2))/(1 - x**2) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False