Existence and Uniqueness of Solutions of Ordinary Differential Equations
 Existence and Uniqueness of Solutions of Ordinary Differential Equations
 Ordinary Differential Equations ODE Home General Terms First Order ODE Separable Exact Linear Implicit Existance & Uniqueness Higher Order ODE Systems of ODE Sturm-Liouville Transform Methods Numerical Methods Resources Bibliography

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 Existence and Uniqueness of Solutions 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