Consider the following system of equations that model the strange dynamics between the two populations of Planet Math: x(t) denotes the population of the mathvillagers and y(t) denotes the population of the biocitizens; t is in years. d = y³ −0.5x² dt dt = y²x³ + 2 Let S(t) = (xs(t), ys(t)) be the solution of the system that goes through the point (2, 0.5) at some time to. Which of the following is true? O Immediately after to, both populations increase. O Immediately after to, the population of mathvillagers to decrease and that of the biocitizens to increase. O Immediately after to, the population of biocitizens to decrease and that of the mathvillager to increase. O Immediately after to, both populations increase.

Should I take the dy/dx of both first or divide them first? Please explain the answer alongside the steps. Thank you!