61.29.13 problem 122

Internal problem ID [12622]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-4
Problem number : 122
Date solved : Tuesday, January 28, 2025 at 03:23:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2 n} \left (b \,x^{n}+c \right )^{m}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y&=0 \end{align*}

✗ Solution by Maple

dsolve(x^2*diff(y(x),x$2)+(a*x^(2*n)*(b*x^n+c)^m+1/4-1/4*n^2)*y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[x^2*D[y[x],{x,2}]+(a*x^(2*n)*(b*x^n+c)^m+1/4-1/4*n^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved