Information for the Math 3350 Final
The problems listed below are the types of problems found on your sample and in-class
exams. The best way to prepare for the final is to practice working problems like the ones
on your exams, the book and homework.
1. Find explicit solution to a separable initial value problem.
2. Find explicit solution to a first order linear initial value problem.
3. Find implicit general solution to an exact equation. Or, find an integrating factor and
show it works. Or, given an integrating factor, show it works and solve the equation.
4. Find implicit general solution of a Bernoulli equation y 0 + py = qy n , a homogeneous
equation y 0 = f (y/x), or equation in the form y 0 = f (ax + by + c).
5. Find and classify equilibria for an autonomous equation.
6. Use the fundamental existence and uniqueness theorem to determine interval of existence for a linear initial value problem.
7. Determine whether a set of functions are dependent or independent.
8. Use reduction of order to find a second solution.
9. Find the general solution to a constant coefficient 2nd order homogenous equations
and solve initial value problems.
10. Find the general solution of higher order equation.
11. Find the general solution for a Euler-Cauchy problem.
12. Use undetermined coefficients to find a particular solution and find the general solution
of a non-homogeneous problem.
13. Use variation of parameters to find a particular solution and find the general solution
of a non-homogeneous problem.
14. Find some Laplace transforms (you need 1st and 2nd shift theorems, periodic, etc).
15. Find some inverse Laplace transforms (may need 1st and/or 2nd shift theorems).
16. Find partial fraction and inverse Laplace transform.
17. Solve integral equation.
18. Use Laplace transforms to solve some initial value problems.
19. Given an IVP for an ODE. For a power series solution y(x) =
∞
X
cn xn find the recur-
n=0
rence relation and use it to find the sum of the first several terms in the series.