## Calculus 8th Edition

Published by Cengage

# Chapter 17 - Second-Order Differential Equations - 17.1 Second-Order Linear Equations - 17.1 Exercises: 20

#### Answer

$y(x)=2\frac{2}{5}e^{\frac{-2x}{3}}-2\frac{2}{5}e^{x}$

#### 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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