74.2.17 problem 22

Internal problem ID [15858]
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 : 22
Date solved : Tuesday, January 28, 2025 at 08:10:27 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 14

dsolve([x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+4*y(x)=0,y(1) = 1, D(y)(1) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 15

DSolve[{x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==0,{y[1]==1,Derivative[1][y][1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 \log (x)+1}{x^2} \]