MTH 245 - Exam 3
Name:
1. Solve the following system of linear equations:
(
d2 x
dt2
d2 y
dt2
= 4y + et
.
= 4x − et
2. Consider a spring-mass whose equation of motion is given by x00 +5x0 +4x = 0.
Decide if the system is overdamped, critically damped or underdamped.
3. Compute:
a) L t cos t .
−2s
b) L−1 se2 +16 +
e−4s
s+1
.
Here L denotes the Laplace transform.
4. Use the Laplace transform to solve the initial value problem
 00
 y + 4y = et − sin t
y(0) = 1
 0
y (0) = 0.
5. Use the Laplace transform to solve the following integro-differential equation
0
Rt
y (t) + 6y(t) + 0 y(τ )dτ = 1
y(0) = 0.