In this paper, we present a numerical method using Laguerre polynomials to approximate the answer of generalized pantograph equations with variable coefficients. In this method, we approximate the solution of the pantograph differential equation as a finite series of Laguerre polynomials. Then using the properties of Laguerre polynomials and using appropriate matrix relations and the collocation method, the pantograph equation becomes a set of matrix equations. By solving this system using the given relations, the solution of the pantograph differential equation is obtained. Several numerical examples are provided to illustrate the efficiency and accuracy of the proposed method. The approximate solutions are very close to exact answers, and the error of the present method in numerous numerical examples is very small.
