1. Use Laplace transforms to solve the following differentialequations for ?(?) for ? ≥ 0. Use ?(0) = 0 and ?̇(0) = 1 for eachcase.
i. 0 = ?̈(?) + 2?̇(?) + 4?(?)
ii. 0 = ?̈(?) + 3?̇(?) + 2?(?)
iii. 5 = ?̈(?) + 5?̇(?) + 6?(?)
3. For the three differential equations from problem onedetermine the steady-state value of the system using:
a. lim?→0 ??(?),
b. lim ?→∞ ?(?) analytically,
c. lim ?→∞ ?(?) using MATLAB
Please solve #3 and show MATLAB code
