74.2.6 problem 11

Internal problem ID [15847]
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 : 11
Date solved : Tuesday, January 28, 2025 at 08:09:26 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {\sin \left (\ln \left (x \right )\right ) c_{1} +\cos \left (\ln \left (x \right )\right ) c_{2}}{x} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 22

DSolve[x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 \cos (\log (x))+c_1 \sin (\log (x))}{x} \]