TEXAS A&M UNIVERSITY
DEPARTMENT OF MATHEMATICS
MATH 308-200
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 + 2y 0 + 5y = 13 sin(3t),
y(0) = 0, y 0 (0) = 1.
4.
(10 points)
1. The external force g(t) is equal to a for 0 < t ≤ b and is equal to 0 when t > b.
Express g(t) using the Heaviside function uc (t) and take its Laplace transform.
2. Solve the initial value problem
y 00 + 4y = g(t),
y(0) = 0, y 0 (0) = 0.
3. Find the (simplified) form of the solution y(t) for t > b, substitute b = ε, a = 1/ε
and take the limit ε → 0 (keeping t fixed).
4. Solve the initial value problem
y 00 + 4y = 0,
and comment on similarities.
y(0) = 0, y 0 (0) = 1,
Points:
/25