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Math 221 Differential Equations quiz 1

January 25, 1999, Tom Linton

1. (Fish Population Control with Overcrowding and Harvesting) For the IVP

y ' =

where is a positive constant:

a) What is the overcrowding coefficient? What is the harvesting rate?

b) Find the two equilibrium solutions.

c) The direction field for this IVP is shown below. Sketch in the solution y(t) with y(5) = 5.

2. Solve the following differential equations or IVP's:

a) y ' =

b) y ' + 2y = 3, y(0) = -1.