TEXAS A&M UNIVERSITY DEPARTMENT OF MATHEMATICS MATH 308-502

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TEXAS A&M UNIVERSITY
DEPARTMENT OF MATHEMATICS
MATH 308-502
Exam 2 version A, 25 Oct 2013
On my honor, as an Aggie, I have neither given nor received unauthorized aid on this work.
Name (print):
In all questions no analytical work =⇒ no points!
1.
Solve the initial value problem
y 00 + 5y 0 + 6y = e−3t ,
y(0) = 1, y 0 (0) = 0.
2.
Find the general solution to
y 00 + 9y =
1
.
cos(3t)
3.
Solve the initial value problem
y 00 + 4y = sin(3t),
y(0) = 0, y 0 (0) = 1.
In view of Question 5, it is recommended to use the Laplace Transform method here.
4.
The voltage E(t) supplied to a curcuit is sin(3t) for time 0 ≤ t ≤ π and is swithed off
after time t = π. Express E(t) using the Heaviside function uc (t). Calculate the Laplace
transform of E(t).
5.
Solve the initial value problem
y 00 + 4y = E(t),
y(0) = 0, y 0 (0) = 0,
where E(t) is given in question 4.
Points:
/25
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