Answer
$${y}=c_{1}+c_{2}\exp^{-5x}$$
Work Step by Step
$$y''+5y=0$$Let $y-e^{\lambda{x}}$ so that $(\ln{y})'=\lambda$.
$${\lambda}^2+5{\lambda}=0$$
$$\lambda(\lambda+5)=0$$
$$\lambda_{1,2}=0,-5$$
$$\therefore{y}=c_{1}+c_{2}\exp^{-5x}$$
Elementary Differential Equations and Boundary Value Problems 9th Edition
by Boyce, William E.; DiPrima, Richard C.
Published by
Wiley
ISBN 10:
0-47038-334-8
ISBN 13:
978-0-47038-334-6
Chapter 3 - Second Order Linear Equations - 3.1 Homogenous Equations with Constant Coefficients - Problems - Page 144: 5
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