SOLUTION OF A DIFFERENTIAL-DIFFERENCE EQUATION VIA AN ANSATZ METHOD

The differential-difference equation phi '(t) = alpha phi(t) + beta phi(-t) is a special case of the pantograph equation phi '(t) = alpha phi(t) + beta phi(gamma t) at gamma = -1. The pantograph is the device responsible for gathering the current in electric trains. The present paper develops an ansatz method to solve the current model. The developed ansatz method is capable to obtain the solution in exact wave form which has not been reported in the literature. At special cases of the involved parameters, the obtained exact solutions are in full agreement with the corresponding ones in the literature via a series approach. However, the present method is direct, simpler, and can be further extended to include other complex models of the same type.