## Exam Information

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## Sample Document Text

Math 211
Final Exam
December 3, 2000
Instructions: This is a closed book, three hour exam. Calculators are not allowed. Please give
reasons for all of your answers.
There is a short table of integrals on the last page which might be of help to you.
Print your name:
Print your section number:
Write out and sign the pledge:
1. (8 points) Find the solution to the initial value problem
dy
dt
+ y tan t = cos t · sin t with y(0) = 0.
What is the interval of existence of the solution?
2. (8 points) Solve the initial value problem
x
primeprime
+ 6x
prime
+ 13x = 0 with x(0) = 2,x
prime
(0) =?2.
3. (8 points) Consider the equation
y
prime
= (y
2
+ 2y)(1 + y)
2
.
a) Find and analyze all equilibrium points.
b) Provide a sketch showing the qualitative behavior of all solutions.
4. (10 points) Consider the system
x
prime
= x(1 ? y)
y
prime
= x
2
? y.
a) Find and analyze the equilibrium points.
b) Sketch the nullclines. On your sketch indicate the direction of the vector field alon...

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