Approximate solutions of generalized logistic equation

This study investigates the behavior of the approximate solutions of the generalized logistic equation y' = y (1 - y(alpha)), where alpha > 0. Based on the concept of Ulam stability, a concrete estimate of the amplitude of the difference between the approximate solution and the exact solution is obtained using the comparison principle and some sharp inequalities. The obtained results can be ( ) applied to the nonautonomous Richards model C' = r(t)C(1 - C-alpha/K).