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Let y(x) be a solution of the differenti...

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

A

`Y(-4)=0`

B

`y(-2)=0`

C

y(x) has a `(-1,0)`

D

`y(x) ` has a critical point in the interval `(-1,0)`

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The correct Answer is:
C
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