ABSTRACT
A differential equation is an equation relating some function f to one or more of its derivatives. An example is
d2f
dx2 (x) + 2x
df
dx (x) + f2(x) = sinx . (1)
Observe that this particular equation involves a function f together with its first and second derivatives. Any given differential equation may or may not involve f or any particular derivative of f . But, for an equation to be a differential equation, at least some derivative of f must appear. The objective in solving an equation like (1) is to find the function f . Thus we already perceive a fundamental new paradigm: When we solve an algebraic equation, we seek a number or perhaps a collection of numbers; but when we solve a differential equation we seek one or more functions.
