Question

Let (-c,c) be the largest open interval in $\R$ (where c is either a positive real number or c = ∞) on which the solution y(x) of the differential equation $\frac{dy}{dx}=x^2+y^2+1$ with initial condition y(0) = 0 exists and is unique. Then which of the following is/are true?

• A. y(x) is an odd function on (-c, c).
• B. y(x) is an even function on (-c, c).
• C. (y(x))2 has a local minimum at 0
• D. (y(x))2 has a local maximum at 0

Answer 1

Answer: (A), (C)

y(x) is an odd function on (-c, c).

Answer 2

The correct option is (A): y(x) is an odd function on (-c, c). and (C): (y(x))2 has a local minimum at 0