JEE-Advanced 2015 (14/40)

Let $y(x)$ be a solution of the differential equation $(1+e^x)y'+ye^x=1$ . If $y(0)=2$ , then which of the following statements is(are) true ?

\[\begin{array}{} (1) \, y(-4)=0 \\ (2) \, y(-2)=0 \\ (3) \, y(x) \text{ has a critical point in the interval } (-1,0) \\ (4) \, y(x) \text{ has no critical point in the interval } (-1,0) \end{array}\]
Note :

• Submit your answer as the increasing order of the serial numbers of all the correct options.

• For eg, if your answer is $(1),(2)$ , then submit 12 as the correct answer, if your answer is $(2),(3),(4)$ , then submit 234 as the correct answer.