Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 10 - Introduction to Differential Equations - 10.1 Solving Differential Equations - Exercises - Page 505: 39


$$ y= e^{1-e^{-t}}.$$

Work Step by Step

By separation of variables, we have $$\frac{dy}{y}=e^{-t}dt $$ then by integration, we get $$\ln y=-e^{-t} +c\Longrightarrow y= e^{c-e^{-t}}.$$ Now, since $y(0)=1$, then $c=1$. So the general solution is given by $$ y= e^{1-e^{-t}}.$$
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