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.

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