(a) Show that the substitution z = 1 / P transforms the logistic differential equation P' =...

Question:

(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.