Help with Method of Undetermined Coefficients. I am having trouble solving this problem with the method of undetermined coefficients:
$(\frac{d^2}{dt^2}+2\frac{d}{dt}+5)y=12e^t-34sin(2t)$
Work: To solve the homogeneous equation, I first tried to find the roots of the auxiliary equation, which I believe is $r^2+2r+5=0$. However, I cannot get a clean root here and I am unsure of what to do in this case.  

For $r^2+2r+5=0$, the roots are 
$$r_{1,2} = -1 \pm ~ 2i.$$
This means that:
$$y_h(t)= e^{-t}(c_1  \cos 2t + c_2 \sin 2t)$$
Can you proceed with the particular? Hint, choose:
$$y_p = a e^t + b \cos 2t + c \sin 2t$$
Sub back into original ODE and solve for the constants.
You should get:
$$a = \dfrac{3}{2}, b = 8, c = -2$$
Write:
$$y(t) = y_h(t) + y_p(t)$$
