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The theory of differential equations works because of a class of theorems called existence and uniqueness theorems. They tell us, given an initial value problem, when that IVP has a solution, and if a solution exists, then it also tells us it is unique. We will focus on the Picard or Picard-Lindelof existence and uniqueness theorem which applies to first order differential equation. A key focus will be on the domain on which a unique solution is guaranteed to exist.

0:00 Intro
1:37 Ex: Existence Failing
4:10 Ex: Uniqueness Failing
9:15 Existence & Uniqueness Theorem


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