61.28.41 problem 101

Internal problem ID [12601]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-3
Problem number : 101
Date solved : Tuesday, January 28, 2025 at 03:22:45 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[x*D[y[x],{x,2}]+(a*x^n+b*x)*D[y[x],x]+(a*b*x^n+a*n*x^(n-1)-b)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved