Answer: Continuous and Lipschitz in y (near the initial point).
- A Constant in both x and y near the initial point
- B Continuous and Lipschitz in y (near the initial point)
- C Periodic in x with some fixed, known period
- D Polynomial in both x and y throughout the domain
Correct answer: B. Continuous and Lipschitz in y (near the initial point)
Explanation: Picard-Lindelof theorem: unique solution exists if f is continuous and satisfies Lipschitz condition in y in a rectangle around (x₀,y₀).
The general solution y=Ax² represents an entire FAMILY of curves, one for each value of the arbitrary constant A; a particular solution (fixed by an initial condition) selects exactly one curve from this family.
Concept context
Equations involving derivatives and their solutions