1/18/2013
MATH 4512 - QUIZ 1 - SOLUTIONS
1. (20) Find the solution of the initial value problem using the Laplace transform,
y + y = 2 cos t,
with y (0) = 1,
y (0) = 0
Solution:
You need
Lcfw_f (t) = sLcfw_f (t) y (0),
Lcfw_f (t) = s2 Lcfw_f (t) sf (0) f
2/1/2013
MATH 4512 - QUIZ 2 - SOLUTIONS
1. (20) Consider the initial value problem with impulse functions,
y + y = (t ) (t 3 ),
with y (0) = 0,
y (0) = 0,
(a) (15) Find the solution using the Laplace transform.
(b) (5) Sketch the solution over [0, 4 ].
So
2/15/2013
MATH 4512 - MIDTERM 1 - SOLUTIONS
1. (25) Find the solution of the initial value problem using the Laplace transform,
y + 3y + 2y = f (t),
with
y (0) = 0,
y (0) = 0,
where
1,
if
0 t < 10
0,
f (t) =
if
10 t <
Solution: THe Laplace transform of t