MATH 3503 test 2 review problems
Q1 Solve y 00 + 2y 0 + 5y = 0, y(0) = 2, y 0 (0) = −1 using Laplace transforms.
1
Q2 Solve y 00 − 2y 0 + 2y = 1, y(0) = 1, y 0 (0) = 0 using Laplace transforms.
2
Q3 Find Y (s) if
y 00
+
y0
+
5
4y
= g(t), y(0) = 0,
y 0 (0)
(
t 0≤t<2
= 0, where g(t) =
1 t>2
3
Q4 Solve
y 00
−
3y 0
+ 2y = g(t), y(0) = 0,
y 0 (0)
(
1 0≤t<5
= 0, where g(t) =
0 t>5
4
Q5 Solve y 00 − y 0 = 2δ(t − 1), y(0) = 0, y 0 (0) = 0.
5


3 2 4
Q6 Solve ~x0 = A~x if A = 2 0 2
4 2 3
6
Q7 Solve
~x0
1 −1
= A~x if A =
5 −3
7