Power series solutions of linear differential equations with polynomial coefficients (Q1099311)

Let y be a formal power series solution of a linear differential equation with polynomial coefficients and y be the nth partial sum of y. It is shown that there exists a linear differential equation (depending on n) which is satisfied by both y and \(y_ n\). This result is applied to show that there exists an algebraic differential equation (independent of n) which is satisfied by y and every \(y_ n\).