d)Choose oneChoose oneAllOne or moretinm (c) What conclusion can be drawn about coefficients in the system ofhomogeneous differential equations satisfied by x1) and x(2)?Choose oneof the coefficients of the ODE in standard formmust be discontinuous at to(d) Find the system of equations x' = P(t)x.1P(t)=

Given: X'=Ptx To find: Solution

Answered: (c) What conclusion can be drawn about…

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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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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(c) What conclusion can be drawn about coefficients in the system of homogeneous differential equations satisfied by x¹) and x(²)? Choose one of the coefficients of the ODE in standard form must be discontinuous at to = (d) Find the system of equations x' = P(t)x. P(t) =