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Daniela tried to solve the differential equation $\frac{d y}{d x}=2 x \cdot e^{-y}$. This is her work:$\newline$$$\frac{d y}{d x}=2 x \cdot e^{-y}$$$\newline$Step $1$: $\quad \int e^{-y} d y=\int 2 x d x$$\newline$Step $2$: $\quad-e^{-y}=x^{2}+C_{1}$$\newline$Step $3$: $\quad e^{-y}=-x^{2}+C$$\newline$Step $4$: $\quad \ln \left(e^{-y}\right)=\ln \left(-x^{2}+C\right)$$\newline$Step $5$: $\quad-y=\ln \left(-x^{2}+C\right)$$\newline$Step $6$: $\quad y=-\ln \left(-x^{2}+C\right)$$\newline$Is Daniela's work correct? If not, what is her mistake?$\newline$Choose $1$ answer:$\newline$(A) Daniela's work is correct.$\newline$(B) Step $1$ is incorrect. The separation of variables wasn't done correctly.$\newline$(C) Step $2$ is incorrect. Daniela didn't integrate $e^{-y}$ correctly.$\newline$(D) Step $4$ is incorrect. The right-hand side of the equation should be $\ln \left(-x^{2}\right)+C$.