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