Calculus (3rd Edition)

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

Chapter 3 - Differentiation - Chapter Review Exercises - Page 164: 72


$$\frac{dy}{dx}=\frac{y+2x}{1-x}, \quad x\neq 1.$$

Work Step by Step

Simplify the given equation first by multiplying both sides by $ x $; We then have $ y=x^2+xy $. Now, by differentiating the equation $ y=x^2+xy $ with respect to $ x $, we get $$\frac{dy}{dx}=2x+y+x \frac{dy}{dx}\Longrightarrow \frac{dy}{dx}(1-x)=y+2x $$ and hence $$\frac{dy}{dx}=\frac{y+2x}{1-x}, \quad x\neq 1.$$
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