What form should the particular solution of a 2nd order linear non homogeneous differential equation take when the right hand side is a constant? if the differential differential equation has the form Ay''+By'+Cy = g(x) where g(x) is a constant what form should the particular solution take? I know if g(x) is an exponential the "trial" solution should be A(e^x) If g(x) is trigonometric it should be A(sin(x))+B(cos(x)) And If it is a polynomial of degree n it should be A(x^n) + B(x^(n-1)) ... +C(x^0) But what if the differential equation is just Ay''+By'+Cy = D Should the trial solution be a polynomial of degree 0? So I would try y = D y' = 0 y'' = 0 which would leave me with CD=D which is useless Please Help! Thanks!