Math 3200 Sample Exam #3
Briggs' Section - Spring 1998

The real exam will have a long sermon here about doing your own work, not collaborating with anyone about the exam, and showing all of your work.

1. Find the general a solution of three of the following ODEs.
   1. .
   2. .
   3. y''(t)+10y'(t)=1+t.
   4. .
2. Find the value of b that gives critical damping in the oscillator equation y''(t)+by'(t)+25y(t) = 0.
3. Consider the ODE .
   1. Classify the ODE in terms of linearity, order and constant/variable coefficient.
   2. Use a trial solution of the form , where p is to be determined, to find the general solution.
   3. Find the solution that satisfies the initial conditions y(1)=1 and y'(1)=0.
4. Consider the oscillator equation
   1. Briefly (in 2-3 words) describe the physical meaning of when this ODE models an oscillator.
   2. Let b=2, , , and A=5. Use Laplace transforms to solve the ODE subject to the initial conditions y(0)=1 and y'(0)=0.
5. You have worked excitedly to solve three initial value problems using Laplace transforms. You are almost done and ready to impress your boss, except that you still need to do the inversion step. Find the inverse Laplace transforms of the following functions.