# tut13 - The University of Sydney Math1003 Integral Calculus...

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The University of Sydney Math1003 Integral Calculus and Modelling Semester 2 Exercises for Week 13 2011 Assumed Knowledge Objectives (12a) To be able to rewrite two coupled frst-order diFerential equations as a single second- order diFerential equation. (12b ) To be able to sketch the solutions o± second-order diFerential equations with constant coe²cients. Preparatory Questions 1. Two species, struggling to compete against each other in the same environment, have populations at time t x ( t ) and y ( t ), satis±ying the equations x ( t ) = 3 x ( t ) - 4 y ( t ) , y ( t ) = - 2 x ( t ) + y ( t ) . ³ind the second-order diFerential equation satisfed by x ( t ). Practice Questions 2. ³ind x ( t ) and y ( t ) in Preparatory Question 1. 3. Two species are in a predator-prey relationship. Let the predator species number Y , and the prey species number X individuals. Historically the numbers o± these species have been constant at X = 3000 and Y = 1500. A±ter a severe environmental

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## This note was uploaded on 09/01/2011 for the course YEAR 1 taught by Professor Various during the Three '11 term at University of Sydney.

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tut13 - The University of Sydney Math1003 Integral Calculus...

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