Q:

Find the general solution to the ode?

$y′′+5y′+6y=85 e^{6x}\cos2x$
What is the general solution to this?
I got..
$y(x)=Ae^{−2x}+Be^{−3x}$
then doing it again i got a different answer.
$y(x)=Ae^{−x}+Be^{−2x}+86e^{2x}\sin3x$
What is the correct answer if it is either of these if not what is it?

A:

hint: The particular solution $A_p = Me^{6x}\cos (2x) + Ne^{6x}\sin (2x)$. Can you plug it into the ODE and solve for $M,N$? And the general solution is: $A_g = A_h + A_p = Ae^{-2x}+ Be^{-3x} + Me^{6x}\cos (2x) + Ne^{6x}\sin (2x)$.

