Chapter 2
The General, Linear Equation
Let a1 (x) , a2 (x) , . . . , an (x) be continuous functions dened on the interval
a x b, and suppose u (x) is n-times dierentiable there. We form from
u the function Lu, dened as follows:
(Lu) (x) = u(n) (x) + a1 (x
1.1 First Order Differential Equations
1.1.0
Introduction
We begin the study of differential equations with a number of definitions:
Definition: A differential equation is an equation that contains the derivative of one or
more dependent variables with re