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M 408S Worksheet: Separable differential equations Work your problems on a separate sheet of paper. 1. Find the general solution to each differential equation. (a) (b) dy dx dy dt = xe−y = 10 − 2y (c) (y 2 + xy 2 )y 0 = 1 2. Find the general and particular solutions to each differential equation. (b) du dt dy dx (c) dy dx (a) = 2t+sec2 t , 2u = ln x , xy u(0) = −5 y(1) = 2 p = 2x 1 − y 2 , y(0) = 0 3. For problem 2 (c), is there more than one particular solution? If the initial value had been y(0) = 2, what would have happened? 4. Suppose a population grows according to a logistical model with initial population 1000 and carrying capacity 10,000. If the population grows to 2,500 after one year, what will the population be after another three years? 1