55.34.3 problem 241

Internal problem ID [14014]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-8. Other equations.
Problem number : 241
Date solved : Thursday, October 02, 2025 at 09:08:55 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{n} y^{\prime \prime }+c \left (a x +b \right )^{n -4} y&=0 \end{align*}

✗ Maple

ode:=x^n*diff(diff(y(x),x),x)+c*(a*x+b)^(n-4)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x^n*D[y[x],{x,2}]+c*(a*x+b)^(n-4)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
n = symbols("n") 
y = Function("y") 
ode = Eq(c*(a*x + b)**(n - 4)*y(x) + x**n*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False