61.33.4 problem 242

Internal problem ID [12663]
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 : 242
Date solved : Monday, March 31, 2025 at 06:49:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

TypeError : Add object cannot be interpreted as an integer