Consider a first order differential equation

with the initial condition

where is bounded in the neighborhood of the initial point, i.e.,

in

Sufficient Condition of Existence: If is continuous in the neighborhood region , the solution of this initial value problem in the region exists.

Sufficient Condition of Existence and Uniqueness: If and its partial derivative with respect to are continuous in the neighborhood region , the solution of this initial value problem in the region exists and is unique.

Picard Iteration Method: The unique solution of the above initial value problem is

where