MA 238-01
§1.1–1.3 Quiz #1 score
Name:
11 June 2000
1. Suppose the differential equation
y=22y−y2−40
represents the rate of change of a population
yat time t≥0. Determine all equilibrium
solutions. Sketch those solutions on the axes
to the right, then sketch solution curves for
a few other initial populations: say, y(0)=
1,3,9,15,22? Explain. (10 points)
t
y
2. Use the method of integrating factors to find the general solution to the given differential
equation. Explain what happens to the solutions as tgets large. Then find the particular
solution with the property y(0)=1. (10 points)
dy
dt =−2ty −4t