The undetermined coefficients method, also called the method of undetermined coefficients, solves certain nonhomogeneous linear ordinary differential equations with constant coefficients by choosing a trial particular solution with unknown coefficients. When the forcing term is a finite combination of polynomials, exponentials, sines, and cosines, the trial solution is chosen from the same family. If that form overlaps a solution of the corresponding homogeneous ordinary differential equation, it is multiplied by a sufficient power of the independent variable. Substitution into the original ordinary differential equation and comparison of coefficients then determine the unknowns. The general solution is
 |
where 
solves the homogeneous ordinary
differential equation and 
is the determined particular
solution.
