Modifying DTM to solve nonlinear oscillatory dynamics

The lack of DTM in oscillatory dynamics will be cured using the Sin and Cos after Treatment (SAT and CAT). The use of Direct Transformation Method (DTM) to solve linear and nonlinear differential equations will be given first. The DTM outcome is equated with the Taylor series. For even and odd powers terms expressions incorporating the Cos and Sin functions are respectively used. For highly nonlinear dynamics when both odd and even powers are in presence, both trigonometric functions simultaneously are suggested to be used. Some examples are given to show the details and the effectiveness of the suggestion.