Consider a second order nonhomogeneous, linear differential equation of the form: a^2y'' + a^1y' + a^0y = g(x)
where y is the dependent function which is a function of the independent variable x; ao, a1, and a2 are constant coefficients; and g(x) is called the input function Using the Method of Undetermined Coefficients requires a guess for the particular solution, yp(x), based on the form of the input function.
Match each guess for the particular solution, yp(x), with its appropriate input function g(x).
A. yp(x) = (Ax + B) cos(3x) + (Cx + D) sin(3x)
B. yp(x) = A cos(3x) + B cos(2x) + Csin(3x) + Dsin(2x).
C. yp(x) = A cos(3x) + B sin(3x).
D. yp(x) = Ae^x cos(2x) + Be^xsin(2x).
E. Does not match any of the options.
1. g(x) = cos(2x) + sin(32).
2. g(x) = xcos(3x).
3. g(x) = cos(3x).
4. g(x) = e^x sin(2x).
5. g(x) = xsin(2x).