Answer
Confirmed, See explanation.
Work Step by Step
To confirm $y = 3e^{x^3}$ is the solution, differentiate y first,
$y = 3e^{x^3}$
$y' = 3e^{x^3}.3x^2$
$y' = 9x^2e^{x^3}$
Since $ y = 3e^{x^3}$,
$y' = 3x^2y$
Where y(0) = 3 by inspection
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 8 - Mathematical Modeling With Differential Equations - 8.1 Modeling With Differential Equations - Exercises Set 8.1 - Page 566: 1
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