DUE TONIGHT PLEASE HELP ME ASAP!!! Consider the initial value problem

$y^{\text{'}\text{'}}25y=cos(5t),y(0)=7,y^{\text{'}}(0)=3.$

a$.$ Take the Laplace transform of both sides of the given differential equation to create the cerresponding 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 $($until you get to part $($b$)$ below$).$

$$

b$.$ Solve your equation for $Y(s).$

$Y(s)=L\{y(t)\}=$

c$.$ Take the inverse Laplace transform of both sides of the previous equation to solve for $y(t).$

$y(t)=$