61.27.22 problem 32

Internal problem ID [12532]
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 : 32
Date solved : Tuesday, January 28, 2025 at 03:20:13 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

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

Not solved