On Approximate Euler Differential Equations

Abstract

We solve the inhomogeneous Euler differential equations of the form $x^2{y}^{\prime \prime }(x)+\alpha x{y}^{\prime }(x)+\beta y(x)={\sum }_{m=0}^{\infty }{a}_m{x}^m$ and apply this result to the approximation of analytic functions of a special type by the solutions of Euler differential equations.