3. Solve the following differential equations by using LaPlace
transformation:
2x'' + 7x' + 3x = 0; x(0) = 3, x'(0) = 0
x' + 2x = ?(t); x(0-) = 0
where ?(t) is a unit impulse input given in the LaPlace
transform table.
Solve the differential equation y'' − y' − 2y = 9e^2t , with
initial conditions y(0) = 3, y' (0) = −2, using two different
methods. Indicate clearly which methods you are using. First
method:
Second method:
1. Use Laplace transforms to solve the following differential
equations for ?(?) for ? ≥ 0. Use ?(0) = 0 and ?̇(0) = 1 for each
case.
i. 0 = ?̈(?) + 2?̇(?) + 4?(?)
ii. 0 = ?̈(?) + 3?̇(?) + 2?(?)
iii. 5 = ?̈(?) + 5?̇(?) + 6?(?)
3. For the three differential equations from problem one
determine the steady-state value of the system using:
a. lim?→0 ??(?),
b. lim ?→∞ ?(?) analytically,
c. lim ?→∞ ?(?)...