61.33.11 problem 249

Internal problem ID [12749]
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 : 249
Date solved : Tuesday, January 28, 2025 at 04:17:40 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved