Undamped oscillator with driving force

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just wondering how to go about this one:
An undamped harmonic oscillator is subject to a driving force [tex]F_0e^{-bt}[/tex]. It starts from rest at the origin (x=0) at time t=0.

assuming a general solution [tex]x(t)=A cos(\omega t - \phi) + Be^{-\alpha t}[/tex] where A, [tex]\omega[/tex], [tex]\phi[/tex], B, and [tex]\alpha[/tex] 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
[tex]ma=-kx + F_{driving}[/tex] however i cannot see how i can solve for all the constants with these two equations..any help?
 

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