61.33.20 problem 258

Internal problem ID [12758]
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 : 258
Date solved : Tuesday, January 28, 2025 at 04:18:08 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

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

Not solved