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* [[Peano existence theorem]] guarantees the existence of a local solution to any initial value problem for an explicit first-order first-degree differential equation <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 is continuous in an open rectangle containing the point.