# Changes

## First-order first-degree differential equation

, 19:21, 1 July 2012
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Note that the process may involve some slight change in the set of solutions. In particular, any solution that ''identically'' satisfies both $P(x,y) = 0$ and $Q(x,y) = 0$ may be lost when we normalize. In most cases, there are no such solutions, and there are usually at most finitely many such solutions.

==Existence and uniqueness of solutions==

* [[Peano existence theorem]] guarantees that existence of a local solution to any initial value problem for a first-order first-degree differential equations $\frac{dy}{dx} = G(x,y)$ with initial value point $(x_0,y_0)$ provided that $G$ and $\partial G/\partial y$ are continuous in an open rectangle containing the point.
* [[Picard-Lindelof theorem]] establishes existence and uniqueness under somewhat stronger continuity and differentiability assumptions.
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