Calculus (3rd Edition)

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

Chapter 10 - Introduction to Differential Equations - Chapter Review Exercises - Page 526: 10


$$ y=\sqrt{2(\ln x+2-\ln 3) }.$$

Work Step by Step

By separation of variables, we have $$ y dy= x^{-1}dx $$ then by integration, we get $$ \frac{1}{2}y^{2}=\ln x+c .$$ Now, since $y(3)=2$, then $c=2-\ln 3 $. So the general solution is given by $$ y=\sqrt{2(\ln x+2-\ln 3) }.$$
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