Question: (a) Show that the substitution z = 1 / P transforms the logistic differential equation P' = kP(1 - P / M) into the linear

(a) Show that the substitution z = 1 / P transforms the logistic differential equation P' = kP(1 - P / M) into the linear differential equation
z' + kz = k / M
(b) Solve the linear differential equation in part (a) and thus obtain an expression for P(t). Compare with Equation 9.4.7.

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a z 1 P P 1 z P z z 2 Substituting into P kP1 P M gives us z z 2 k 1 z 1 1 zM z kz 1 ... View full answer

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