61.31.7 problem 188

Internal problem ID [12688]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-6
Problem number : 188
Date solved : Tuesday, January 28, 2025 at 03:39:03 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime }+x \left (a \,x^{n}+b \right ) y^{\prime }-\left (a \,x^{n}-a b \,x^{n -1}+b \right ) y&=0 \end{align*}

✗ Solution by Maple

dsolve(x^3*diff(y(x),x$2)+x*(a*x^n+b)*diff(y(x),x)-(a*x^n-a*b*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^3*D[y[x],{x,2}]+x*(a*x^n+b)*D[y[x],x]-(a*x^n-a*b*x^(n-1)+b)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved