Math 3200 Final Exam
Briggs' Section - Spring 1998

This is a two-hour in-class exam. You are allowed to have a page of notes. Write on separate pages and show all of your work. Full credit cannnot be given unless you show complete solutions. Good luck!

1. (12 points) Find the solution of two of the following initial value problems.
   1. 
   2. .
   3. .
2. (6 points) A clay pot is taken out of a pottery kiln at a temperature of 300 degrees and placed in a room with a temperature of 100 degrees. The temperature of the pot as it cools is determined by Newton's Law of Cooling which says that the rate of change of the temperature is proportional to the temperature difference between the pot and its surroundings. Thus,

   

   1. Find the solution of the initial value problem.
   2. What is the steady state temperature of the pot?
3. (12 points) Find the general solution of the following ODEs.
   1. .
   2. .
4. (6 points) Give a answer and a brief explanation for the following questions.
   1. What is y'(0) for the power series solution ?
   2. Is the ODE linear or nonlinear?
   3. Is a fundamental set for the ODE y''(t)+4y(t)=0?
   4. Is a fundamental set for the ODE y''(t)-4y(t)=0?
   5. How many arbitrary constants appear in the general solution of the ODE ?
5. (7 points) Use Laplace transforms to solve the following initial value problem.

   

6. (7 points) Find the first four terms of the power series solution of the initial value problem

   

   HAVE A GOOD SUMMER!