Ordinary Diff. Eqs. Chapter 1

A. Review: Basics of Linear ODE's.

1. Standard form: linear ODE of nth order

y = yH +yP

yP(x) = particular solution

yH(x) = homogeneous solution

Homogeneous equation has n linearly independent solutions u1,u2,u3 ... un and

2. Linearly independent functions

Set of functions

are linearly independent on the interval a <= x <= b. if the equation

B. Advanced ODE's