# Undamped oscillator with driving force

An undamped harmonic oscillator is subject to a driving force $$F_0e^{-bt}$$. It starts from rest at the origin (x=0) at time t=0.

assuming a general solution $$x(t)=A cos(\omega t - \phi) + Be^{-\alpha t}$$ where A, $$\omega$$, $$\phi$$, B, and $$\alpha$$ are real constants, find the position x(t) as a function of time.

I was thinking to take this general solution, differentiate, and apply initial conditions to the two equations, however all i could solve for is alpha in terms of omega.
Then i thought to differentiate again and plug into the equation
$$ma=-kx + F_{driving}$$ however i cannot see how i can solve for all the constants with these two equations..any help?