Please show the solutions to how it came to the answers using Laplace Transform. Thank you.

Solve the following differential equations using Laplace transform. 1. y' - y = 1; y(0) = 1 Ans: y = 2e* - 1 2. y'+ 2y = t; y(0) = 2 Ans: e -2t + NIK t 3. y"ty =0; y(0) =0, y'(0) = 1 Ans: y = sint 4. y" ty = t'; y(0) = 1, y'(0) =0 Ans: y = t- + 3 cost - 2 5. y" + 4y = sin 2t; y(0) =0, y'(0) = 0 4 Ans: y = -=t cos 2t + = sin 2t 8