61.28.43 problem 103

Internal problem ID [12603]
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 : 103
Date solved : Tuesday, January 28, 2025 at 03:22:47 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

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

Not solved