61.33.9 problem 247

Internal problem ID [12747]
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 : 247
Date solved : Tuesday, January 28, 2025 at 04:17:35 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

dsolve(x^n*diff(y(x),x$2)+(a*x^n-x^(n-1)+a*b*x+b)*diff(y(x),x)+a^2*b*x*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^n-x^(n-1)+a*b*x+b)*D[y[x],x]+a^2*b*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved