Answer
False
Work Step by Step
As a counterexample, consider the differential equation $\frac{dy}{dx}=\frac{1}{xy}$ can be solved by separation of variables but $y=0$ is not a solution.
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 6 - Differential Equations - 6.3 Exercises - Page 423: 81
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