  A coupled two frequency Hill's equation is solved. Analytically approximate
solution correct up-to first order is derived using modified Lindstedt Poincare
perturbation method. For a wide range of controlling parameters we compare the
numerical and analytical solutions. The solution is the first step towards
developing a comprehensive understanding of the electrodynamics of charged
particles in a combinational ion trap utilizing both electrostatic DC and RF
fields along with a constant static magnetic field with prospects of confining
antimatter such as anti hydrogen for a reasonably long durations of time.
