Existence and Uniqueness Theorems

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Multiple Choice

Consider the differential equation $\frac{dy}{dx} = y^2 + 1$. Which of the following statements is true?

  1. The equation has a unique solution for any initial condition.
  2. The equation has a unique solution for some initial conditions.
  3. The equation has no solutions.
  4. The equation has infinitely many solutions.
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