Elementary Differential Equations and Boundary Value Problems 9th Edition

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: 2



Work Step by Step

$$y''+3y'+2y=0$$Let $y-e^{\lambda{x}}$ so that $(\ln{y})'=\lambda$. $${\lambda}^2+3{\lambda}+2=0$$ $$(\lambda+2)(\lambda+1)=0$$ $$\lambda_{1,2}=-2,-1$$ $$\therefore{y}=c_{1}\exp^{-2x}+c_{2}\exp^{-x}$$
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