{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Assignment 4

# Assignment 4 - Professor Jason Levy University of Ottawa...

This preview shows page 1. Sign up to view the full content.

Professor Jason Levy, University of Ottawa, MAT 1332C, Winter 2011 Assignment 4, due Monday March 7, 10:00am at the beginning of class. Late assignments will not be accepted; nor will unstapled assignments. Student Number DGD section By signing below, you declare that this work was your own and that you have not copied from any other individual or other source. Signature Student Name 1. (a) Find the equilibrium solutions of the following differential equations. You should find three y 0 = y 3 - 6 y 2 + 11 y - 6 . (b) Draw the phase line diagram. (c) Graph the equilibrium solutions and sketch the solutions curves for the following initial conditions: y (0) = 0 , y (0) = 0 . 5 , y (0) = 1 . 5 , y (0) = 2 . 5 , y (0) = 4 . You should clearly indicate the behaviour of the solution curves as t → ∞ . 2. Suppose that size N if a populations satisfies the following differential equation: dN dt = 5 N 2 1 + N 2 - 2 N. (a) Find all equilibrium points. (b) Use the derivative criterion to decide if the equilibria are stable or unstable.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}