The population dynamics for prey-predator model of owl and rat is representated by follow- ing differential equation 4 = 4y1 – 42 2 = 2yı + 42 Find the general solution of this system.Then find the formula if y (0) = 2 and y2(0) = 5.

Solve the system of differential equations Jx¹= x'= - 4x + 21y y=0x + 3y x(0) = 6, y(0) = 2 x(t) = y(t) =

Solve the system of differential equations - 3x + 0y - 12x + 1y x' l y' = || x(0) = 3, y(0) = 10 x(t) = -3e3t y(t) = 6e3t + e5t

Solve the system of differential equations Jx'= -23x + 72y y'= -6x + 19y x(0) = -6, y(0) = -1 x(t) = y(t) =

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…

Solve the following system of differential equations (x¹ = 2x + 3y y' = 2x + y 2.-

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