Consider the initial value problem

$$y^{\,\prime\prime} - 9 y = e^{-t}, \ \ \ y(0) = 1, \ \ \ y^{\,\prime}(0) = y_0^{\prime}.$$
Suppose we know that $y(t) \to 0$ as $t \to \infty$. Determine the solution and the unknown initial condition.

$y(t) =$ help (formulas)

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