Hello, I am learning about the general solution to higher order linear non-homogeneous differential equations. I know that the general solution of such an equation is of the form ##y=y_h+y_p## where ##y_h## is the solution to the respective homogeneous equation and ##y_p## is a particular solution of the equation. I also realize that in the homogeneous solution, you want to include as many terms as possible, even giving a parameter of constants to each of these terms to include as many different solutions as possible. My question is, why do we only need one particular solution? If we are trying to make our general solution as "general" as possible, why do we not include a family of solutions that satisfy the non-homogeneous differential equation?