61.31.27 problem 208

Internal problem ID [12708]
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 : 208
Date solved : Tuesday, January 28, 2025 at 03:58:32 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\left (\alpha \gamma +\beta \right ) x +\beta \lambda \right ) y^{\prime }-\left (\alpha x +\beta \right ) y&=0 \end{align*}

✗ Solution by Maple

dsolve((a*x^3+b*x^2+c*x+d)*diff(y(x),x$2)+(alpha*x^2+(alpha*gamma+beta)*x+beta*lambda)*diff(y(x),x)-(alpha*x+beta)*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^3+b*x^2+c*x+d)*D[y[x],{x,2}]+(\[Alpha]*x^2+(\[Alpha]*\[Gamma]+\[Beta])*x+\[Beta]*\[Lambda])*D[y[x],x]-(\[Alpha]*x+\[Beta])*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out