I have a series RLC circuit with an equation:
$$\frac{d^2I}{dt} + 2\alpha \frac{dI}{dt} + \omega_0^2 I = 0$$
(No outside sources affecting the circuit, only some $I_0$ was in the circuit at the beginning)
The result is, for overdamped response ($\alpha^2 - \omega_0^2 > 0$):
$$I = Ae^{(-\alpha - \sqrt{\alpha^2 - \omega_0^2})t} + Be^{(-\alpha - \sqrt{\alpha^2 - \omega_0^2})t}$$
So, if $I(0) = I_0$ then $A+B = I_0$, but that still doesn't solve A and B completely. What other initial conditions do i have to include or what other things do i have to do in order to find A and B completely?