Hello. Please answer the following question, ensure that your answer is correct and is supported by calculations, explanations and algebraic work. Try to only utilize the sections/topics seen below. Solutions for Ordinary Differential Equations must be given in real values form(i.e. no complex or imaginary values). Please organize your work, in a reasonably neat and coherent way. Again, ensure to justify your answer in a clear and reasonable way, as well as in a detailed manner. Answers not supported or justified will receive a thumbs down. Thank you so much, I hope you have a great day! :) Topics potentially utilized in the following question:

? Section 2.1: Separate and Integrate ? Section 2.2: Slope Fields ? Section 2.3: Integrating Factors ? Section 2.4, Section 6.1: Existence, Uniqueness, and Eulers Method ? Section 2.7: The Phase Line ? Section 3.1: 2nd order linear ODE?Section 3.2: 2nd order homogeneous linear ODE ? Section 3.4: 2nd order nonhomogeneous linear ODE ? Section 3.3: Damped Mass-Spring System ? Section 3.5: Forced Oscillators ? Section 3.5: added detail for steady state ? Section 3.5: Beats and Resonance ? first order linear (autonomous) systems ? linear systems II (like phase planes and direction fields) ? linear systems III(like eigenvalues and eigenvectors) ? linear systems IV (like rewriting undamped oscillators as a system, using eyelets principle and linearity principle, classification of equilibrium point ? Linear systems V (eigenvalues, trace of a matrix) ? Systems (evecs) ? Nonlinear systems ? Equilibrium point analysis ? parameters in non linear systems/Bifurcation ? Equilibrium Point analysis failure & Qualitative Analysis

For the following model: dx = x(40 - 2x - 2y) dt dy dt = y(60 - 4x - 2y) Notice that x and y are both non-negative. 1. Find all equilibria. Il. For the equilibrium (ac* , y* ) with a* > 0 and y* > 0: I. Compute the Jacobian Matrix Il. Determine the type of the equilibrium point