Vipul: Created page with "==Statement== Consider a first-order differential equation in explicit form (note that any [[first-order first-degree differential equa..."

2012-07-09T02:41:09Z

Created page with "==Statement== Consider a first-order differential equation in explicit form (note that any [[first-order first-degree differential equa..."

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==Statement==

Consider a [[first-order differential equation]] in [[explicit differential equation|explicit form]] (note that any [[first-order first-degree differential equation]] can be converted to such a form):

<math>\frac{dy}{dx} = G(x,y)</math>

Suppose <math>G</math> is a [[continuous function]] (in a jointly continuous sense) on an open subset of <math>\R^2</math> containing a point <math>(x_0,y_0)</math>. Then, there exists a function <math>f</math> defined on an open subset <math>I</math> of <math>\R</math> containing <math>x_0</math> such that <math>f</math> satisfies the initial value problem, namely:

<math>f(x_0) = y_0 \qquad \mbox{ and } f'(x) = G(x,f(x)) \ \forall \ x \in I</math>

Peano existence theorem - Revision history

Vipul: Created page with "==Statement== Consider a first-order differential equation in explicit form (note that any [[first-order first-degree differential equa..."