Calculus (3rd Edition)

Published by W. H. Freeman

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

Answer

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

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

After 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.