The system of first order differential equations:has solution:Yı(t)Y2 (t)=1/2==3 y₁ + 2y2,-34 y₁ - 13 y2,Note: You must express the answer in terms of real numbers only.31 (0) = 432 (0) = -20

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Answered: The system of first order differential…

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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Determine the solution of the differential equation y- 6y" + 12y-8y = 0 y = C,e 2x + C,xe-2x + C,x2e 2x + C3x?e 2x a. b. y = C,e2x + C2x²e2x + C3x³e2x с. y = C,e2x + C,xe²x + C3x²e* d. y = C,e¯* + C,e2* + C3x²e2*
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The population dynamics for prey-predator model of owl and rat is representated by follow- ing differential equation 1 = 4y1 – Y2 2 = 2yı + Y2 Find the general solution of this system.Then find the formula if y1(0) = 2 and y2(0) = 5. %3D
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Consider a system of differential equations describing the progress of a disease in a population, given by In our particular case, this is: a) Find the nullclines (simplest form) of this system of differential equations. The x-nullcline is y = x = 3-3xy - 1x y = 3xy - 2y where x (t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals. The y-nullclines are y = and x = b) There are two equilibrium points that are biologically meaningful (i.e. whose coordinates are non-negative). They are (x1,9₁) and (x2, y2), where we order them so that x1 < x2. The equilibrium with the smaller x-coordinate is (x₁, y₁) : The equilibrium with the larger x-coordinate is (x2, y₂) = where A = 0 sin (a) c) The linearization of the system of differential equations at the equilibrium (ï1, Y₁) gives a system of the form (+) ¹ (~), f əx ∞ a Ω = A x' G E = F(x, y) for a vector-valued function…
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The system of first order differential equations: y/2 = = 3 y₁ + 2y2, -34 yı 13 y2, - 3₁ (0) = 4 32 (0) = -20