Let \( y(x) \) be a solution of the differential equation \( (1+ \) \( \left.e^{x}\right) y^{\pr...

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Let \( y(x) \) be a solution of the differential equation \( (1+ \) \( \left.e^{x}\right) y^{\prime}+y e^{x}=1 \). If \( y(0)=2 \), then which of the following
P statements is (are) true ?
[JEE Advanced-2015]
W
(a) \( \mathrm{y}(-4)=0 \)
(b) \( \mathrm{y}(-2)=0 \)
(c) \( y(x) \) has a critical point in the interval \( (-1,0) \)
(d) \( \mathrm{y}(\mathrm{x}) \) has no critical point in the interval \( (-1,0) \)
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