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 504: 9


(a), (b), and (d) are separable.

Work Step by Step

(a) is separable, $$ y'=f(y)g(x); \quad f(y)=9y^2, \quad g(x)=1/x.$$ (b) is separable, $$ y'=f(y)g(x); \quad f(y)=e^{3y}, \quad g(x)=\sin x/\sqrt{4-x^2}.$$ (c) is not separable (notice the addition sign). (d) is separable, $$ y'=f(y)g(x); \quad f(y)=9-y^2, \quad g(x)=1.$$
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