|Existence and Uniqueness Theorem| State and proof
Автор: Adeyemi Adedayo
Загружено: 2026-01-09
Просмотров: 25
Описание:
The Existence and Uniqueness Theorem for differential equations guarantees that an Initial Value Problem (IVP) has one, and only one, solution in a given region, provided the function and its partial derivative (for first-order equations) are continuous in a neighborhood around the initial point (x₀, y₀). This theorem ensures that solution curves don't cross, preventing multiple solutions from the same starting point, and confirms a solution exists even if it can't be found analytically, as long as conditions are met.
Key Concepts
Initial Value Problem (Existence: A solution exists for the IVP).
Uniqueness: Only one solution exists.Conditions
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