Assignment:
Q1. Solve y''+4y'+4y=g(t) using Laplace transforms.... y(0) = 2; y'(0)=-3. Express the answer in terms of a convolution integral.
Q2. Find the inverse of F(s) = 1/[(s^4)(s^2+1)] the answer can be left as a convolution integral.
Q3. Solve y''''+5y''+4y=g(t) using laplace transforms.... y(0) = 1; y'(0)=y''(0)=y'''(0)=0. Express the answer as a convolution integral.
Q4. Find the inverse of F(s) = 1/[(s+1)(s^2+4)] the answer can be left as a convolution integral.
Provide complete and step by step solution for the question and show calculations and use formulas.