Topics review for Chapter 3.

1. Solving ay’’+by’+cy= 0, given initial condition.

Find behavior of the solution when t tends to infinity (∞,-∞, decaying oscillation or growing oscillation). Find maximum, minimum of the solution.
-See for example 3.4.11-3.4.14, pb 1 of this, pb1a of this

2. Find a differential equation whose general solution is y =…
See for example 3.1.17, 3.1.18

3. Solving Euler equations

See for example 3.3.35 - 3.3.42, 3.4.41 - 3.4.46.

4. Use method of reduction of order to find a second solution

See for example 3.4.23 - 3.4.30, pb 2 of this, pb 5 of this

5. Find or guess a particular solution of nonhomogeneous equation ay’’+by’+cy=g(t) where g(t) is a polynomial, exponential, sine, cosine or sum of these functions

-pb 2 of this; pb1b, pb2 of this,

6. Find the general solution of nonhomogeneous equations

-pb 1 of this, pb 4 of this

7. Find the solution of nonhomogeneous equations with initial condition.

-pb 2 of this,

8. Spring-mass system

-pb 3, 4 of this; pb 3, 4 of this; pr 3, 4 of this