61.28.44 problem 104

Internal problem ID [12604]
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 : 104
Date solved : Tuesday, January 28, 2025 at 03:22:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

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

Not solved