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