## anonymous 5 years ago can anyone help me find the analytical soln to dQ/dt = K(A-Q)

1. anonymous

This is a separable ordinary differential equation. $\frac{dQ}{dt}=K(A-Q) \rightarrow \frac{dQ}{A-Q}=K{dt}$Then integrating,$\int\limits_{}{}\frac{dQ}{A-Q}=\int\limits_{}{}Kdt \rightarrow -\ln{(A-Q)}=Kt+C$where C is a constant. Then,$A-Q=e^{-Kt}e^C=Be^{-Kt}$where B is just the constant e^C. So,$Q=A-Be^{-Kt}$

2. anonymous

Thank you very much. this make it alot clearer. :)

3. anonymous

No worries. Feel free to 'fan' me =)

4. anonymous

No problems, but how do i star you? sorry im new to this.

5. anonymous

I think there should be something like, "become a fan" next to my name...and I think you just saw it 'cause my 20 turned to 21.

6. anonymous

Done. thanks again

7. anonymous

No probs.