D. Basic Facts Of Ordinary Dierential Equations

We will review some basic facts of ordinary dierential equations of the rst and second order.

A dierential equation of the rst order is an equation of the form

(D.1) F (x; y; y0) = 0;

where F is a given function of three variables. A solution of (D.1) is a dierentiable function f(x) such that

F (x; f(x); f 0(x)) = 0;

for all x in the domain (interval) where f is dened. The general solution of (D.1) is the set of all solutions of (D.1).