Answer
See the details below.
Work Step by Step
Since $ y=25e^{-2x^2}$, then
$$ y'=-100xe^{-2x^2}.$$
Now, by substitution of $ y $ and $ y'$ into the equation, we verify that $y$ is a solution of the given differential equation.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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: 5
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