Find the transform of the given function - solve the ivp by

Question

1. Find the transform of the given function

Note: Must show all work to earn credit

2. Use Laplace trasnform of derivatives to find the transform of f(t) if f(t) = cos²(2t)

3. Use Laplace trasnform of integrals to find the inverse transform of 1/s(s-2)²

Must show all details of your work for credit

4. Solve the IVP by the Laplace transform. Must show all details of your work for credit

y" - y' = e^tcost, y(0) = 0, y'(0) = 0

5. Solve the shifted data IVP by the Laplace transform Show at Marls of your work

y"-2y'-3y =0, y(4)= -3, y'(4)= -17

6. Use Laplace transform to find the initial value problem for current in the given RLC -circuit zero initial current and charge.