Explain the answer please with steps

4. Solve the initial-value problem y" + 4y - sin(2t), y(0) = 0, y'(0) = 0. Answer: Apply the Laplace transform to the equation: 2 2 $ 2 Y ( S ) + 4 Y (s ) = $2 + 4 Y (s) = ( $ 2 + 4 ) 2 Using Example 1.55 from the textbook (see the problem above ) with a = 2, we obtain 2 . 23 y ( t ) = [- 1 3 $2 + 22) 2 sin (2t) - 2t cos(2t) ]