Let y(x) be a solution of the differential equation (1+ex)y′+yex=1. If y(0)=2, then which of the following statements is (are) true? [JEE(Advanced) 2015]
(A) y(−4)=0
(B) y(−2)=0
(C) y(x) has a critical point in the interval (−1,0)
(D) y(x) has no critical point in the interval (−1,0)