Solución particular de una ecuación diferencial ordinaria de Cauchy Euler no homogénea de tercer orden aplicando el método lineal ECA

In this investigation, the particular solution of a third-order non-homogeneous ordinary Cauchy Euler differential equation will be found, which has the form x^3 y^'''+x^2 y^''=f(x) in which the linear ECA method will be used, which consists of changing the variable y^'', in order to solve it as a first-order linear differential equation, the result of which is integrated twice in terms of the dependent variable and thus obtain the particular solution that is exactly the same as that obtained analytically by any mathematical method or that determined using mathematical software.