Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 17 - Second-Order Differential Equations - 17.1 Second-Order Linear Equations - 17.1 Exercises - Page 1200: 12

Answer

$y(x)=c_{1}e^{-3x}cos(5x)+c_{2}e^{-3x}sin(5x)$

Work Step by Step

First write the current derivatives as $y''$ etc., this is to make it easier. It is not obliged. After this you substitute the $y'', y'$ and $y$ with $y''=r^{2}e^{rx}, y'=re^{rx} and y=e^{rx}$. And by filling out the equation you can find the final equation.
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