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: 43


$$ y= \sin^{-1}(e^{x-\ln 2})= \sin^{-1}(e^{x}/2).$$

Work Step by Step

By separation of variables, we have $$\frac{\cos y}{\sin y}dy=dx $$ then by integration, we get $$ \ln(\sin y)=x+c .$$ Now, since $y(\ln 2)=\pi/2$, then $c=-\ln 2$. So the general solution is given by $$ y= \sin^{-1}(e^{x-\ln 2})= \sin^{-1}(e^{x}/2).$$
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