Find yc(complimentary solution) and set up yp(particular solution) by the method of undetermined coefficients.
y''+y'+(1/2)y = x*e^(-x/2)+x*cos(x/2)
yc = c1 e^(-x/2) cos(x/2) + c2 e^(-x/2) sin(x/2)
Finding yp is confusing me. Could someone please explain how to come to the answer. What assumptions must be made?
yp =(Ax + B)e^(-x/2) + (Cx+D)cos(x/2) + (Ex + F) sin(x/2)