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Existence and Uniqueness Theorems
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Consider the differential equation $\frac{dy}{dx} = y^2 + 1$. Which of the following statements is true?
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A
The equation has a unique solution for some initial conditions.
💡 Explanation:
The equation is Lipschitz continuous in $y$, so it has a unique solution for any initial condition in a sufficiently small interval. However, the equation is not globally Lipschitz continuous, so it may not have a unique solution for all initial conditions.