Final Exam — Math 220 — December 12, 2005
Name:
Directions:
Show all your work on these papers, using the back if necessary, and circle your
answers if that’s appropriate. The Laplace transforms you need are on the blackboard. Remember
that if you’ve made it this far, you can do all of these problems.
1. (10 pts) Solve the inital value problem (IVP)
x
+
1
t
x
= cos(
t
);
x
(
π
2
) = 1
2. (10 pts) The population
N
of a certain species is modeled by the differential equation
dN
dt
=

(
N

10)(
N

100)
.
Find the equilibrium points and classify them as stable or unstable. Plot some approximate
representative solutions
N
(
t
) for initial conditions lying between 0 and 150.
3. (15 pts) Find the general solution to
x

3
x
+2
x
= 2 sin(2
t
). Use the method of undetermined
coefficients for the inhomogeneous equation. Identify the transient and steadystate solutions.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
4. (10 pts) When a 1 gram mass is attached to a spring, it displaces the spring 10 cm from its
equilibrium position.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 LERNER
 Math, Differential Equations, Equations, Force, Friction, Mass, Eigenvalue, eigenvector and eigenspace

Click to edit the document details