61.33.4 problem 242

Internal problem ID [12742]
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 : Tuesday, January 28, 2025 at 04:17:28 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*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[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,y[x],x,IncludeSingularSolutions -> True]
 

Not solved