A Particular Solutions Formula For Inhomogeneous Arbitrary Order Linear Ordinary Differential Equations, 2nd Ed

A particular solution for any inhomogeneous linear second, third, and fourth order ordinary differential equation is generally determined. Applying what was determined thus, and following by example a particular solution formula for arbitrary order is obtained and proved. Finding a particular solutions to a linear inhomogeneous ordinary differential equation has always been a process of determining homogeneous solutions, and then adding any particular solution of the inhomogeneous equation. The well-known methods of undetermined coefficients and variation of parameters have long been the standard in determining this particular solution. The former has sometimes been considered 'ad-hoc', and both can be intricate. A relatively simple formula is determined and proved, here, which allows the particular solution to be written and evaluated immediately. A pair of examples for second, third, and fourth orders, as well one each of orders five and six are presented here, in detail – all corroborated by texts or it's own construction. Further, a small table of particular solutions of inhomogeneous second order linear ordinary differential equations is manifested.