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: 17

Answer

$y(x)=cos(\sqrt{3}x)+\frac{3}{\sqrt{3}}sin(\sqrt{3}x)$

Work Step by Step

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. After this you use the given $y(0)=a$ and $y'(0)=b$ in order to find the two constants.
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