54.3.15 problem 1015

Internal problem ID [12310]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1015
Date solved : Wednesday, October 01, 2025 at 01:43:02 AM
CAS classification : [_Titchmarsh]

\begin{align*} y^{\prime \prime }-\left (a^{2} x^{2 n}-1\right ) y&=0 \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

TypeError : Mul object cannot be interpreted as an integer