Answer
False
Work Step by Step
As a counter-example, consider the first-order differential equation $xy'-2y=0$.
$y=x^2$ is a solution to this equation but $y=x^2+1$ isn't.
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 - 6.1 Exercises - Page 406: 89
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