2. Given the system of differential equations a' = 0.2x -0.005xy, y'= -0.5y +0.01.xy, which models the rates of changes of two interacting species populations, describe the type of x- and y-populations involved (exponential or logistic) and the nature of their interaction (competition, cooperation, or predation). Then find and characterize the system's critical points (type and stability). Determine what nonzero x- and y-populations can coexist. Then construct a phase plane portrait that enables you to describe the long term behavior of the two populations. Use https://www.geogebra.org/m/utcMvuUy to confirm your results.

Q: Convert the differential equation u' '+ 5u' – 3u = e letting a = u, y = u' into a system of first…

A: To convert the differential equation into a system of first order equations by letting c=u and y=u'

Q: What is an autonomous differential equation? What are its equilibrium values? How do they differ…

A:

Q: Transform the given differential equation into an equivalent system of first-order differential…

A: Given Differential equation  .Transform into system of first order differential equation .

Q: A  system is modelled by the following simultaneous equations: 6.2a+ 7.9b + 12.6c = 18 7.5a + 4.8b…

A:

Q: We saw that in the nonlinear system of differential equations: %3D the quantity 1 1 1 (7, 4) = ;v° +…

A: Given the level curves of the nonlinear system of equations as Hx,y=y22+x22-x33. We need to find the…

Q: The system of non-linear differential equations * = sin a cos y, y = sinz - siny, has an equilibrium…

A: Given: System of non-linear differential equations x˙=sinxcosy y˙=sinx-siny Equilibrium point of…

Q: Z₁' (t) = -6₁2 + 1.12₁ -0.822 Z₂²' (t) = -13.8 +2.12, -1.222 Z₁ (0) =11 Z₂₁₂ (0) = 4

A: The given system of differential equations are as follows.Find the equalibrium point as follows.Put…

Q: use the method of variation of parameters to find the general solution to the system.  v'(t)=-g -…

A: Differentiating the given equation we get      v"(t) = 0 - 5v'(t) -120(h'(t)/m)              =…

Q: A third-order homogeneous linear equation and three linearly independent solutions are given below.…

A: Given: The differential equation is y3+2y''-y'-2y=0,y(0)=4, y'(0)=4 and y''(0)=0. It is also given…

Q: Convert the differential equation u'' - u' – 2u = e-5t into a system of first order equations by…

A: Given: u''-u'-2u=e-5t

Q: we are given a second-order non-homogeneous linear differential equation: mh''+5h'+120h=mg with…

A: The objective of the question is to convert a second-order non-homogeneous linear differential…

Q: Find the amount of salt in the tank at any time. What is the equilibrium solution of the modeling…

A: Given that  A tank contains 500 L of water with 10 kg of dissolved salt. Salt water containing 0.05…

Q: Find the solution to the linear system of differential equations x(0) = 3 and y(0) = 5. x(t):…

A:

Q: For the nonlinear autonomous system x' = y? + 2y , y' = x – y

A: Given nonlinear autonomous system x'=y2+2yy'=x-y For critical point put y'=0 and x'=0.

Q: Convert the differential equation u'+ 3u' + 2u = e" into a system of first order equations by…

A:

Q: n electrical network can be modelled using a system of first order linear differential quation given…

A:

Q: The system of non-linear differential equations x = -sin x cos y, y = sin x + sin y, has an…

A: Given system of non-linear first order system of differential equations are