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: 38


$$ y= \frac{4}{1-t}.$$

Work Step by Step

By separation of variables, we have $$\frac{dy}{y}=\frac{dt}{1-t}$$ then by integration, we get $$\ln y=-\ln (1-t)+\ln c=\ln\frac{c}{1-t}\Longrightarrow y= \frac{c}{1-t} .$$ Now, since $y(2)=-4$, then $c=4$. So the general solution is given by $$ y= \frac{4}{1-t}.$$
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