Suppose that a fourth order differential equation has a solution $y = -2e^{4x}x\cos\!\left(x\right)$. Find the initial conditions that this solution satisfies.

$y(0)$	=
$y^{\,\prime}(0)$	=
$y^{\,\prime\prime}(0)$	=
$y^{\,\prime\prime\prime}(0)$	=