Gompertz equation: dy/dt = ry * ln(K/y), where r, K > 0 are constants.

Quadratic approximation of the Gompertz equation: dy/dt = r(y K) (r/2K) *(y K)^2 .

(a) For each equation, sketch a graph of the right-hand side function (i.e. Gompertz: f(y) = ry ln(K/y), Approximation: f(y) = r(y K) (r/2K)* (y K)^2 ), versus y. Find the equilibrium solutions and determine their stability.

(b) Find the general solution to each equation.

(c) Given the initial condition y(0) = K/2 , what is the long-term behavior of the solution to each equation?