# JEE-Advanced 2015 (14/40)

**Calculus**Level 3

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.