Mathematics / Engineering Mathematics Topic: Ordinary Differential Equations
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Equations satisfying the condition
F(x, y, y', y'', ..., y^(n)) = 0
Existence and uniqueness A foundational theoretical result is the Picard–Lindelöf theorem (also called the Picard existence and uniqueness theorem), which states that for the initial-value problem y' = f(t,y), y(t0)=y0, if f is Lipschitz continuous in y and continuous in t on a neighborhood of (t0,y0), then a unique local solution exists. For linear systems with continuous coefficients, solutions exist and are unique on any interval where the coefficients are defined. Understanding these conditions helps determine whether a modeled system is well-posed. Your best legal bets are:
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