MA 238-02
§3.1–4.2, 6.1–6.2
Test #2
Take-home part score
Name:
26 April 1999
Instructions: Work the following problem and turn it in no later than noon on Thursday, April
29, 1999. You may use Maple or other inanimate resources to check you answer or to help you
along the way but you must show all of your work so that the solution appears to have been done
completely by hand. The work you turn in must be completely your own.
Problem: Use the method of Laplace transforms to find the solution to the IVP
y ++5y+4y=2u5(t) cos(t−5),y(0)=1,y
(0)=0
where u5(t) denotes the unit step function step(t−5) in the book’s notation and Heaviside(t−5)
in Maple’s notation. Also sketch (or include computer printout) the graph of the solution on the
t-interval [0,6π]
Note: If you use Maple, you can use the dsolve function to solve the IVP. There is an option
method=laplace you can give dsolve that will force Maple to use the method of Laplace transforms.
This will increase the probability that Maple’s answer will be in the same form as yours. Maple
also has laplace and invlaplace functions for calculating Laplace and inverse Laplace transforms
respectively. Enter ?laplace and ?invlaplace for help on these functions in Maple.