The system of differential equations 1 dx x dt 1 dy = 1- x - y y dt y 2 2' model the interaction of two populations x and y. (a) What kind of interaction do these equations describe? ? (Symbiosis takes place when the interaction of two species benefits both. An example is the pollination of plants by insects.) (b) Now suppose that we start with the initial populations (x(0), y(0)) = (1, 1.5). What happens to the populations in the long run? (For each, enter infinity or a numerical value.) x goes to y goes to

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