Abstract
Our goal is to give a very simple, effective and intuitive algorithm for the solution of initial value problem of ODEs of 1st and arbitrary higher order with general i.e. constant, variable or nonlinear coefficients. We find a local expansion of the differential equation/function that employs the higher derivatives (in the sense of total derivatives) of the differential equation/function with respect to independent variable to find an approximation which can be successively improved to desired accuracy by adding extra terms. The method can also be used easily for general 2nd and higher order ODEs. We explain with examples the steps to solution of initial value problems of 1st order ODEs and later follow with more examples for linear and non-linear 2nd order ODEs.
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