Answer
$y=x^2-x^3+4x+1$
Work Step by Step
The anti-derivative for $\dfrac{d^2y}{dx^2}=2-6x$ is $\dfrac{dy}{dx}=2x-3x^2+c$ and $y=x^2-x^3+cx+c'$
Now, apply Initial conditions $y'(0)=4 ; y(0)=1$, we have
This implies, $0-0+c=4$ and $0+c'=1 \implies c'=1$
Hence, $y=x^2-x^3+4x+1$
