Q.31 let (-c, c) be the largest open interval in r (where c is either a positive real number or c = o) on which the solution y(x) of the differential equation :

Q.31 Let (-c, c) be the largest open interval in R (where c is either a positive real number or c = o) on which the solution y(x) of the differential equation := x2+y2+1 with initial condition y(0) = 0 o1o exists and is unique. Then which of the following is/are true? (A) y(X) is an odd function on (-c, c). (B) yx) is an even function on (-c, c). (C) (yx))has a local minimum at 0. (D) (yx)) has a local maximum at 0.