Consider the initial value problem I' + 3r = 45t, r(0) = 2. a. Take the Laplace transform of both sides of the given differential equation to create the coresponding algebraic equation. Denote the Laplace transform of r(t) by X. 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 X (s). X(s) = L {r(t)} = c. Take the inverse Laplace transform of both sides of the previous equation to solve for r(t). (You should perform some partial fractions work first before you can calculate the inverse Laplace via the table.) r(t) =

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