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 statements is (are) true ?
Select ALL correct options:
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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