Question: The following system of differential equations represents the interaction between two populations, x and y. (a) Describe how the species interact. How would each species

The following system of differential equations represents the interaction between two populations, x and y.

dx dt dy dt = 3x+2xy =-y+5xy

(a) Describe how the species interact. How would each species do in the absence of the other? Are they helpful or harmful to each other?
(b) If x = 2 and y = 1, does x increase or decrease? Does y increase or decrease? Justify your answers.
(c) Write a differential equation involving dy∕dx.
(d) Use a computer or calculator to draw the slope field for the differential equation in part (c).
(e) Draw the trajectory starting at point x = 2, y = 1 on your slope field, and describe how the populations change as time increases.

dx dt dy dt = 3x+2xy =-y+5xy

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