Question: Consider the initial value problem y'+ 36y =cos(6t), y(0)=2, (0)=09. a. Take the Laplace transtorm of both sides of the given differential equation to create

Consider the initial value problem y'+ 36y =cos(6t), y(0)=2, (0)=09. a. Take the Laplace transtorm of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transtorm 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). = help (formulas) 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(). y(t) = y" + 36y = cos(6t), y(0) = 2, y'(0) = 9. 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 (until you get to part (b) below). S $2Y - 2s - 9+36Y = A help + 36 (formulas) b. Solve your equation for Y(s). Y(s) = [ty(t) } c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y( t) =

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