Find the general integral of the equation
and the particular solution through the circle
We are given the following partial differential equation (PDE) to solve: \[ (x - y)p + (y - x - z)q = z \] where \(p = \frac{\partial z}{\partial x}\) and \(q = \frac{\partial z}{\partial y}\), and we are tasked with finding the general solution of this ___ _________ ___ _______ _________ ________.
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Do the functions y1 (t) = and
form a fundamental set of solutions of the equation
, on the interval
? Justify your answer.
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Show that the minimum rate of growth will occur when the population is equal to half the equilibrium size, that is, when the population is b / 2a
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