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
For the function f(x) = x^2 +3x / 2x^2 + 7x +3 find the
following, and use it to graph the function.
Find: a)(2pts) Domain
b)(2pts) Intercepts
c)(2pts) Symmetry
d) (2pts) Asymptotes
e)(4pts) Intervals of Increase or decrease
f) (2pts) Local maximum and local minimum values
g)(4pts) Concavity and Points of inflection and
h)(2pts) Sketch the curve
Solve the following constant coefficient linear differential
equations using Laplace Transform (LT), Partial Fraction Expansion
(PFE), and Inverse Laplace Transform (ILT). You must check
answers in the t-domain using the initial conditions.
Note: Complex conjugate roots
y ̈ (t) + 6 ̇y (t) + 13y (t) = 2
use the initial conditions
y(0) = 3, ̇y(0) = 2.