#### Answer

$y=2e^{-x}+2x-1$

#### Work Step by Step

Here, $y=\int (-2e^{-x}+c) dx$
Now, we have $y=2e^{-x}+cx+c'$
Apply the initial conditions $y(0)=1$
We get $c'=-1$ and $y'(0)=0 \implies c=2$
Thus, we have $y=2e^{-x}+2x-1$

Published by
Pearson

ISBN 10:
0321999584

ISBN 13:
978-0-32199-958-0

$y=2e^{-x}+2x-1$

You can help us out by revising, improving and updating this answer.

Update this answerAfter you claim an answer you’ll have **24 hours** to send in a draft. An editor
will review the submission and either publish your submission or provide feedback.