Method of Undetermined Coefficients

Term in F(x)	Corresponding terms in yp
Cx^k	A0 + A1x + …. + Akx^k
Ce^mx	Ae^mx
C cos(Bx) or C sin(Bx)	C1 cos(Bx) + C2 sin(Bx)

If a term of y_p coincides with a term of the homogeneous solution, multiply the term in y_p by the smallest power of x that removes the duplication.

Substitute y_p and its derivatives into the nonhomogeneous equation and solve for the coefficients.