Circuit equation proof?

In a certain question managed to get to:





R*(dQ/dt) + (1/C)*Q = 0





In the answers it then says:





Q(t) = Q*e^-(t/RC)





I know this is true, obviously, but don't understand the jump between the two steps, does he integrate it, how?





Cheers!

Circuit equation proof?
SORRY I FORGET TO intergrate from Q0 to Q!!





subtract (1/c)Q on the other side


R(dQ/dt)=-Q/C


its a separable differential equation so you need the Q on the other side.


R(dQ/Q)(1/dt)=-1/C


(dQ/Q)(1/dt)=-1/RC


dQ/Q=-dt/RC


intergrate dQ from Q0 to Q and


intergrate dt from 0 to t so


lnQ/Q0=-t/RC


take the e on both sides


Q=Q0e^(-t/RC)


Q is a function of time so


Q(t)=Q0e^(-t/RC)


SORRY I FORGET TO intergrate from Q0 to Q!!


if you need any more help just ask.