The unique solution to the initial value problem

$$y^{\,\prime} + y = g(t), \ \ \ y(0) = y_0,$$
is $y(t) = 3e^{-4t}-6t+5$. Determine the constant $y_0$ and the function $g(t)$.

$y_0 =$ help (numbers)

$g(t) =$ help (formulas)