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