Questions Asked in Previous 10 Years' Exams Let \( y(x) \) be a solution of the differential equ...

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Questions Asked in Previous 10 Years' Exams
Let \( y(x) \) be a solution of the differential equation \( \left(1+e^{x}\right) y^{\prime}+y e^{x}=1 \). If \( y(0)=2 \), then which of the following statement(s) is/are true?
[More than One Correct 2015]
(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 \( (-1,0) \)
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