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Marcus tried to solve the differential equation $\frac{d y}{d x}=\frac{1}{3 x^{2} y^{2}}$. This is his work:$\newline$$$\frac{d y}{d x}=\frac{1}{3 x^{2} y^{2}}$$$\newline$Step $1$: $\quad \int 3 y^{2} d y=\int \frac{1}{x^{2}} d x$$\newline$Step $2$: $\quad y^{3}=-\frac{1}{x}+C$$\newline$Step $3$: $\quad y= \pm \sqrt[3]{-\frac{1}{x}+C}$$\newline$Is Marcus's work correct? If not, what is his mistake?$\newline$Choose $1$ answer:$\newline$(A) Marcus's work is correct.$\newline$(B) Step $2$ is incorrect. Marcus didn't integrate $3 y^{2}$ correctly.$\newline$(C) Step $3$ is incorrect. Marcus forgot to add a constant to the right-hand side at the end of the process.$\newline$(D) Step $3$ is incorrect. The right-hand side of the equation should be $\sqrt[3]{-\frac{1}{x}+C}$.