Homework 9 (MATH 2310-04) Name (Print):
Due date: Tuesday, April 28, 2009
1. Find the inverse Laplace transform of the given functions (you may need partial
fractions for doing this).
)4s(s
12s4s8
)s(F)c
4s3s
2
)s(F)b
4s
3
)s(F)a
2
2
2
2
:Solution
a) f(t) = 1.5 sin(2t)
b) f(t) = (2 / 5) (et e4t)
c) f(t) = 3 + 5 cos(2t) 2 sin(2t)
2. Use the Laplace transform to solve the given initial value problem.
1)0('y,2)0(y,0y5'y2''y
:Solution
y(t) = 2 et cos(2t) + et sin(2t) / 2.
3. Use the Laplace transform to solve the given initial value problem.
4,0)0('y,1)0(y),t2cos(y''y 22
:Solution
y(t) = (2 4)1 [(2 5) cos(t) + cos(2t)]