61.27.43 problem 53

Internal problem ID [12553]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-2
Problem number : 53
Date solved : Tuesday, January 28, 2025 at 03:21:24 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

dsolve(diff(y(x),x$2)+(a*b*x^n+2*b*x^(n-1)-a^2*x)*diff(y(x),x)+a*(a*b*x^n+b*x^(n-1)-a^2*x)*y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved