<![CDATA[This article discusses how to obtain the Taylor polynomial solution of a higher order linear differential and difference equation with variable coefficients whose initial conditions are known. The process begins by assuming the solution of a higher order linear differential and difference equation in the form of polynomial Taylor. Then it is followed by presenting this equation and its initial conditions in the form of a matrix. This matrix is changed into an augmented matrix. Taylor polynomialsolutions of a higher order linear differential and difference equations is obtained by solving the augmented matrix using elementary row operations.]]>
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