We can apply Laplace transform to an ODE in t with given initial values to form an algebraic equation in Fur), the Laplace transform of the solution. Then we solve the equation to get the Laplace transform of the solution. Finally, we apply the inverse Laplace transform to get the solution of the IVP. This question is on the second half of the process. We rst resolve F(s) into partial fractions, then apply the inverse Laplace transform to get the solution of the IVP. This is a two-part question. 433226343 is (a) The correct form for the partial fraction decomposition of 33 2 5-2 33 L 34 In. + to Q 3 s2 3+4 (b) The Laplace transform of the solution t} of an initial value problem is given by F(s) _ 45 8(35) + ( 18 10)e_33_ (35)2+25 (35)2 +25 34 s3 By taking the inverse of the Laplace transform nd and the enter the function f (it) below in maple syntax. fftl= l Note: Use t) to denote the Heaviside function