The state variable approach of modern control theory provides a uniform and powerful method of representing systems of arbitrary order, linear or nonlinear, with time-varying or constant coefficients.

The paper investigates the solution of a class of linear homogeneous differential equations with varied coefficients and methods of decreasing order of the DE.

In this paper, the truncation errors of the height anomaly and vertical deflection are estimated, and the approximate expressions of the higher order truncation coefficients are derived.