Previous Problem Problem List Next Problem (1 point) Consider the initial value problem $$ y^{\prime \prime} +9 y=\cos (3 t), \quad y()=7, \quad y^{\prime} (0)=9 \text {. } $$ a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of $y(t)$ by $Y(s)$. Do not move any terms from one side of the equation to the other (untili you get to part (b) below). $=$ help (formulas) b. Solve your equation for $Y(s)$. $$ Y(s)=\mathcal{L}|{y(t) = $$ c. Take the inverse Laplace transform of both sides of the previous equation to solve for $y(t) $. $$ y(t)= $$ CS.VS. 1600