The Existence and Uniqueness Theorem for Solutions to ODEs
A slecture by Yijia Wen
2.0 Abstract
Before starting this tutorial, you are supposed to be able to:
· Find an explicit solution for $ \frac{dy}{dt}=f(t) $. This is the same thing as finding the integral of $ f(t) $ with respect to $ t $.
· Know the difference between general solution and a solution satisfying the initial conditions.
· Check one function is a solution to an ODE.
· Distinguish ODE and PDE, know the usual notations.
· Know the basic concepts of ODEs (order, linearity, homogeneity, etc).
2.1 Concept
From the example from 1.1, here we still suppose that we had a linear equation $ ax+b=0 $ with respect to $ x $.
