Consider the system of differential equations dx = 0.3x – 0.02xy - dt dy 0.2y + 0.016xy dt 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 Oy decays absent x x helps y x hurts y Oy helps x Oy hurts x

Let U(x) = 3x² - 4x be a potential energy in one dimension. Find and classify the equilibria of the system. 3 If one equlibrium is stable and the other unstable, enter the stable equilibrium first. If both equilibria have the same stability, enter them in either order. x= Stable O Unstable O Stable Unstable 41

Consider the system of non-linear differential equations dx dt dy dt - = Select one: - x sin y, Select the option that gives the Jacobian matrix for this system. -y sin x. sin x x cos y x cos y - sin x x sin y -y sinx sin y -y cos x y cos x sin y -y cos x sin y sin y -y cos x x sin y -y sin x x cos y - sin x - sin x x cos y

Consider the system of non-linear differential equations  dx/dt = x2 - 2x - y2 + 1,  dy/dt = xy - 3x.  What is the complete list of equilibrium points for this system?