Consider the system of differential equations da = -0.5x -0.013xy dt -0.4y+0.019xy Where x and y represent two populations interacting. Select all the following that are true. x grows absent y x decays absent y y grows absent x y decays absent x x helps y x hurts y y helps x y hurts x dy = dt

Consider the following system of differential equations describing two populations: æ' = 0.02a (1 – ) + 0.004xy 80 (1 y' = 0.04y(1 ) - 0.0002xy 20 a. Describe what the equations tell us about the populations (how the populations behave absent interaction, and how interaction affects each population). b. Find all equilibrium points algebraically. c. Classify each equilibrium using linearization d. Sketch some solution curves in the phase plane (x-y plane)

Give the substitution that converts the given nonlinear equation into a linear equation then find the general solution y'-y=-y² a. y(x) = b. y(x)= d. y=3 e. y² = c. y(x) = - O a 1 1+ Ce=t e 2 1+e-2x 1 e'[t+1+e] t6 + 1 2t3 5t 2+5Ct5

Transform the given system of differential equations into an equivalent system of first-order differential equations. x' - 3x' - 5x+2y=0 y'' +6y' - 6x-3y = sin t Let x₁ = x, X₂ = X', Y₁ = y, and y₂ = y'. Complete the system below. X₁' X₂ X Y2 II 11 11 11