Undetermined Coefficients

Set up the correct linear combination of functions with undetermined literal coefficients to use in finding a particular integral by the method of UC. (Do not actually find the particular integrals.)

$\displaystyle y''-6y'+8y = x^3+x+e^{-2x}$

$\displaystyle m^2-6m+8=0$

$\displaystyle y_c=C_1e^{2x}+C_2e^{4x}$

$\displaystyle S_1=(x^3,x^2,x,1)$

$\displaystyle S_2=(x,1)$

$\displaystyle S_3=(e^{-2x})$

S_2 is completely contained in S_1 but none are included in the complimentary function?

Thanks.