74.2.5 problem 10

Internal problem ID [15846]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 08:09:24 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }-16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)-16*y(x)=0,y(x), singsol=all)
 

\[ y = x \left (x^{\sqrt {17}} c_{1} +x^{-\sqrt {17}} c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 32

DSolve[x^2*D[y[x],{x,2}]-x*D[y[x],x]-16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^{1-\sqrt {17}} \left (c_2 x^{2 \sqrt {17}}+c_1\right ) \]