I've just started my first class in ODE's and I'm kind of stuck with the idea of asymptotic behavior.
The problem as is follows: Find the general solution and use it to determine the asymptotic behavior for different values of a. $y(0) = a$ as $t\rightarrow$ $+\infty$.
$$y' - \frac{1}{2}y = 2\cos(t)$$
I've solved for the general solution: $$y = \frac{4}{5}(2\sin(t)+\cos(t)) + Ce^{-t/2}$$
Where do I go from here? Thank you for any guidance.