Some Coefficients Method Of Solving Riccati Equation By Lie Group Symmetry

On solving Riccati Equation [1] by symmetry groups  of the form in practice finding the solutions of it , is usually a much more difficult problem solving the Riccati Equation by inspired guesswork, or geometric intuition, the steps used when solving all first order differential equations involve some assumptions and guesses of the form of symmetry for a given differential equation. it is possible to ascertain a particular solution by  linearized symmetry condition[2]for example but these methods take long time for finding parameters Lie group and hard work to make  Simplifying bit and comparing coefficients of powers of equations. Solutions of the Riccati equation with coefficients Are presented. The solutions are obtained by assuming certain relations among the coefficients R(x), Q(x) and P(x) of the Riccati equation, we obtain symmetry cases for the Riccati equation. For each case the general solution of the Riccati equation is also presented.  Of Of the form