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.

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