Question: 3 Obtain the explicit solution to the harvesting problem dN N = N1 EN dt T( K) q subject to the initial condition N (0)

3 Obtain the explicit solution to the harvesting problem dN N = N1 EN dt T( K) q subject to the initial condition N (0) = N0. Here N = N (t) The parameters'r', K ,q, and E are positive constants. Deduce the two limiting behaviors as t > oo. 4 Consider the nonlinear system MATH 456, SPRING 2021 dm 13 a = \"(x $ y) d 1 _y = _$ dt p Assume p > 0. Find all its equilibria and determine their linear stability. 5 Let ,u = 5. Solve the nonlinear system in problem 4 numerically from 5 different initial conditions. Draw the phase portrait. Conclude your nding

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