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Answers without the blur. Sign up and see all textbooks for free! Q. 29

Expert-verified Found in: Page 570 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29–52.29. $\frac{dy}{dx}=3y,y\left(0\right)=4$

The answer is $y\left(x\right)=4{e}^{3x}$

See the step by step solution

## Step 1. Given information

We have been given $\frac{dy}{dx}=3y,y\left(0\right)=4$

## Step 2. Solve using antidifferentiation and/or variable separable method.

The differential equation can be solved by antidifferentiating.

$\int \frac{1}{y}dy=\int 3dx\phantom{\rule{0ex}{0ex}}\mathrm{ln}\left|y\right|=3x+C\phantom{\rule{0ex}{0ex}}y={e}^{3x+C}\phantom{\rule{0ex}{0ex}}y=A{e}^{3x}\left({e}^{c}=A\right)$

Now put $y\left(0\right)=4$,

$4=A{e}^{3\left(0\right)}\phantom{\rule{0ex}{0ex}}4=A$

So, the answer is $y=4{e}^{3x}$ ### Want to see more solutions like these? 