Be careful with the Exp-function method – Additional remarks

It is shown that the solution produced by the Exp-function method may not hold for all initial conditions. Riccati and Maccari nonlinear differential equations are used to illustrate that fact. Conditions of existence for the produced solution in the space of initial conditions and in the space of system’s parameters are derived using the operator method based on the generalized operator of differentiation. The concept of the expansion of an ordinary differential equation is introduced and it is shown that the algebraic–analytical solution of Maccari equation can be produced by solving Riccati equation.