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 ?→∞ ?(?)...
Use the Laplace transform to solve the given system of
differential equations. d2x dt2 + 3 dy dt + 3y = 0 d2x dt2 + 3y =
te−t x(0) = 0, x'(0) = 4, y(0) = 0
Use the Laplace transform to solve the given system of
differential equations.
d2x/dt2 + x − y = 0
d2y/dt2 + y − x = 0
x(0) = 0, x'(0) = −4
y(0) = 0, y'(0) = 1
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.