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Task 1 (Spec 3.f). Consider the following fourth order linear constant coefficient initial value problem. Look at it and enjoy its simplicity. Then solve it. x"" - 5x" + 4x = sin(t) With initial conditions that x(0) = 0, x'(0) = 1, x" (0) = 0 and x"" (0) = 0.

Task 1 (Spec 3.f). Consider the following fourth order linear constant coefficient initial value problem. Look at it and enjoy its simplicity. Then solve it. x"" - 5x" + 4x = sin(t) With initial conditions that x(0) = 0, x'(0) = 1, x" (0) = 0 and x"" (0) = 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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MAT-3304 Due Due: November 7, 2022 DIFFERENTIAL EQUATIONS HomeWork # 11 Fall 2022 November 3, 2022 x' = αx - xy y' = eyxy - By Last Revision Possible: 28 November, 2022 Specification Problems Task 1 (Spec 3.f). Consider the following fourth order linear constant coefficient initial value problem. Look at it and enjoy its simplicity. Then solve it. x" - 5x" + 4x = sin(t) With initial conditions that x(0) = 0, x'(0) = 1, x" (0) = 0 and x"" (0) = 0. Task 2 (Spec 3.g). A Lotke-Volterra system of differential equations models the populations of species in a predator/prey system. That is Species A feeds off of resources in the environment while Species B feeds on Species A. The basic form of the equations is: Where a, ß, y> 0 and 0 <e < 1. Find the equilibrium solutions in terms of a, B, y, e and classify using linearization the stability of each equilibrium. Modify the equations with a harvesting term h which is how many of Species y is harvested per year. How large can h be while there is still a stable equilibrium with positive populations for both x and y? Task 3 (Spec any). Go back and redo any one task you need regardless of the "last revision" date.
Transcribed Image Text:MAT-3304 Due Due: November 7, 2022 DIFFERENTIAL EQUATIONS HomeWork # 11 Fall 2022 November 3, 2022 x' = αx - xy y' = eyxy - By Last Revision Possible: 28 November, 2022 Specification Problems Task 1 (Spec 3.f). Consider the following fourth order linear constant coefficient initial value problem. Look at it and enjoy its simplicity. Then solve it. x" - 5x" + 4x = sin(t) With initial conditions that x(0) = 0, x'(0) = 1, x" (0) = 0 and x"" (0) = 0. Task 2 (Spec 3.g). A Lotke-Volterra system of differential equations models the populations of species in a predator/prey system. That is Species A feeds off of resources in the environment while Species B feeds on Species A. The basic form of the equations is: Where a, ß, y> 0 and 0 <e < 1. Find the equilibrium solutions in terms of a, B, y, e and classify using linearization the stability of each equilibrium. Modify the equations with a harvesting term h which is how many of Species y is harvested per year. How large can h be while there is still a stable equilibrium with positive populations for both x and y? Task 3 (Spec any). Go back and redo any one task you need regardless of the "last revision" date.
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