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Unformatted text preview: Math 104C, Homework 5
1. The system of first order ordinary differential equations: x(t) = 1.2x(t) - x2 (t) - x(t)y(t) , x(t) + 0.2 (1) (2) 1.5x(t)y(t) y(t) = - y(t), x(t) + 0.2 describes a biological prey-predator model, where x(t) measures the size of the prey population and y(t) that of the predators. Solve the system by means of the classical Runge-Kutta method on the interval 0 t 30 with step size h = 0.1. Compute solutions for the two different initial conditions x(0) = 1, y(0) = 0.75 and x(0) = 0.75, y (0) = 0.25 and plot the solution in the (x, y) phase plane. What does the result tell you? ...
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