Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 10 - Introduction to Differential Equations - 10.1 Solving Differential Equations - Exercises - Page 505: 46


$$a= 2,\ \ a=-6$$

Work Step by Step

Given $$y^{\prime \prime}+4 y^{\prime}-12 y=0$$ Since $y=e^{ax}$ is a solution and \begin{align*} y'&=ae^{ax}\\ y''&=a^2e^{ax} \end{align*} Hence \begin{align*} y^{\prime \prime}+4 y^{\prime}-12 y&=0\\ a^2e^{ax}+4ae^{ax}-12e^{ax}&=0\\ [a^2 +4a -12]e^{ax}&=0\\ (a-2)(a+6)e^{ax}&=0 \end{align*} Then $$a= 2,\ \ a=-6$$
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