Answer
Confirmed. See explanation.
Work Step by Step
To confirm $y = \frac{1}{4}x^4 + 2 cos x + 1$ is the solution, differentiate y first,
$y = \frac{1}{4}x^4 + 2 cos x + 1$
$y' = \frac{4}{4}x^3 +(-2 sin x) + 0 $
$y' = x^3 -2 sin x$
Where y(0) = 3 by inspection