Let (-c, c) be the largest open interval in \(\mathbb{R} \) (where c is either a positive real number or \(c = \infty \) ) on which the solution y(x) of the differential equation \(\frac{dy}{dx} = \sin(x) + y^2, \quad y(0) = 0 \) exists and is unique. Then which of the following statements is/are false?
1
y(x) is an odd function on (-c, c) .
2
y(x) is an even function on (-c, c) .
3
\((y(x))^2 \) has a local minimum at x = 0 .
4
\((y(x))^2 \) has a local maximum at x = 0 .