Q.3 Determine the solution of the differential equation y"(t) + y(t) = g(t), y(0) = 1, y'(0) = 1, for t > 0 with g (t ) = sin ( 2t ) , using the Laplace transform. a) Determine Cig(t)}. (Hint: you can use the rules for the Laplace transform from the lecture.) b) Find an algebraic equation for the Laplace transform Y(s) = Cty(t) } of the solution of the IVP and solve for Y (s) to obtain an explicit expression. c) Determine the solution of the IVP y(t) = C-1{Y(s)} by determining its inverse Laplace transform. You may use the partial fraction expansion 2 2/3 2/3 ($2 + 4)($2 + 1) 82 + 1 82 + 4 without verification