Question

can anyone help me find the analytical soln to dQ/dt = K(A-Q)

Answer 1

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,\[Q=A-Be^{-Kt}\]

Answer 2

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

Answer 3

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Answer 4

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Answer 5

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Answer 6

Done. thanks again

Answer 7

No probs.