solve-Mdc-dt-P-km-Cm-where-M-P-m-and-k-are-constant-solve-the-equation-given-C-a-when-t-o-

Question Number 16492 by Sai dadon. last updated on 23/Jun/17

s o l v e

M d c / d t = P + k m - C m w h e r e M . P . m a n d

k a r e c o n s t a n t

s o l v e t h e e q u a t i o n g i v e n C = a w h e n t = o

Answered by mrW1 last updated on 23/Jun/17

\frac{dc}{P + km - mc} = \frac{dt}{M}

\int \frac{dc}{P + km - mc} = \int \frac{dt}{M}

- \frac{1}{m} \ln (P + km - mc) = \frac{t}{M} + U_{1}

- Mln (P + km - mc) = mt + U_{2}

\ln (P + km - mc) = - \frac{m}{M} t + U_{3}

at t = 0 : c = a

\ln (P + km - ma) = U_{3}

\ln (P + km - mc) - \ln (P + km - ma) = - \frac{m}{M} t

\ln \frac{P + km - mc}{P + km - ma} = - \frac{m}{M} t

\frac{P + km - mc}{P + km - ma} = e^{- \frac{m}{M} t}

P + km - mc = (P + km - ma) e^{- \frac{m}{M} t}

\Rightarrow c = \frac{P}{m} + k - (\frac{P}{m} + k - a) e^{- \frac{m}{M} t}

Commented by Sai dadon. last updated on 23/Jun/17

T h a n k s r