Figuring Out a General Solution for RLC Series Circuit

[brainphysics]

So, I have been trying to come up with a general solution for dI/dt in an RLC circuit.

I have attached the work I have done so far. I don't know where but I am making a mistake and the waveform is not coming out right. Would really appreciate a look over my work to see if I made any obvious errors.

 

[Ike Clark]

You did not use the quadratic formula properly. You forgot to square the coefficient R under the radical.