61.29.35 problem 144

Internal problem ID [12565]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-4
Problem number : 144
Date solved : Monday, March 31, 2025 at 05:39:20 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n +2 m}-b^{2} x^{4 m +2}+a m \,x^{n -1}-m^{2}-m \right ) y&=0 \end{align*}

✗ Maple

ode:=x^2*diff(diff(y(x),x),x)+a*x^n*diff(y(x),x)+(a*b*x^(n+2*m)-b^2*x^(4*m+2)+a*m*x^(n-1)-m^2-m)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x^2*D[y[x],{x,2}]+a*x^n*D[y[x],x]+(a*b*x^(n+2*m)-b^2*x^(4*m+2)+a*m*x^(n-1)-m^2-m)*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") 
m = symbols("m") 
n = symbols("n") 
y = Function("y") 
ode = Eq(a*x**n*Derivative(y(x), x) + x**2*Derivative(y(x), (x, 2)) + (a*b*x**(2*m + n) + a*m*x**(n - 1) - b**2*x**(4*m + 2) - m**2 - m)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : Symbol object cannot be interpreted as an integer