  The logistic function is shown to be solution of the Riccati equation, some
second-order nonlinear ordinary differential equations and many third-order
nonlinear ordinary differential equations. The list of the differential
equations having solution in the form of the logistic function is presented.
The simple method of finding exact solutions of nonlinear partial differential
equations (PDEs) is introduced. The essence of the method is based on
comparison of nonlinear differential equations obtained from PDEs with standard
differential equations having solution in the form of the logistic function.
The wide application of the logistic function for finding exact solutions of
nonlinear differential equations is demonstrated.
