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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 <math>P(x,y) = 0</math> and <math>Q(x,y) = 0</math> 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 <math>\frac{dy}{dx} = G(x,y)</math> with initial value point <math>(x_0,y_0)</math> provided that <math>G</math> and <math>\partial G/\partial y</math> are continuous in an open rectangle containing the point.

* [[Picard-Lindelof theorem]] establishes existence and uniqueness under somewhat stronger continuity and differentiability assumptions.