Math 3200 Sample Final Exam
Briggs' Section - Spring 1998

This sample exam is probably longer than a typical two-hour in class exam.

1. Find the general solution of the following three ODEs.

   1. 

   2. 

   3. 

2. The cost of living in a particular country has been rising at 5.5% per year for many years. Assuming this growth rate continues, what is the doubling time for the cost of living?
3. The owners of a fish hatchery harvest and resupply fish in such a way that the fish population obeys the ODE

   

   1. Find the general solution of this ODE.
   2. Find the solution that satisfies the initial condition y(0)=500.
   3. Does the fish population increase or decrease in time? If it increases, find when the fish population reaches 10,000. If it decreases, find when the fish population reaches zero.
4. Which of the following sets of functions are fundamental sets for the ODE y''(t)-16y(t)=0? Explain your reasoning for each case.

   

5. Find the general solution of the following ODEs.

   1. 

   2. 

6. An undamped oscillator is governed by the following initial value problem.

   

   Use Laplace transforms to find the solution of this initial value problem. Make a rough sketch of the solution over three full periods of the solution.

7. Consider the ODE xy''(x)-2y(x)=0. Find a recurrence relation for the coefficients of a power series solution about the point x=0.

7. .