Problem Set 2 (1).pdf - Math 320 Problem Set 2(due September 20 1 The following population model is proposed as an alternative to the logistic model \u0012 \u0013

# Problem Set 2 (1).pdf - Math 320 Problem Set 2(due...

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Math 320: Problem Set 2 (due September 20) 1. The following population model is proposed as an alternative to the logistic model p 0 = 0 . 02 p 1 - p 2 100 (a) Given p (0) = p 0 solve the equation for p ( t ). (b) Sketch the solution curves for several values of p 0 (c) What is lim t →∞ p ( t ) 2. Verify the DE ( t + tan - 1 x ) dt + x + t 1 + x 2 dx = 0 is exact, then find the general solution. 3. Solve the IVP 3 t 2 x 0 = x 2 + 2 t 2 x (1) = 3 4. For the DE x 0 = 5 x 1 + x 2 - x (a) Find the equilibrium solutions and determine their stability. (b) Sketch the solution curves, x(t), for the initial conditions

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