54.3.220 problem 1236

Internal problem ID [12515]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1236
Date solved : Wednesday, October 01, 2025 at 01:46:14 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

TypeError : cannot determine truth value of Relational: _n < x