(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve the euqation [tex] dP/dt = k(M - P)P[/tex] to show that it equals: [tex] P(t) = (MP_{0}) /( P_{0} + (M - P_{0})e^{-kMt})[/tex]

2. Relevant equations

3. The attempt at a solution

[tex] \[ \int \frac {dP} {P(M - P)}\] = k \int dt \ [/tex]

[tex] \frac {1} {M}\ \ln( \frac {P} {M - P}) + C = Kt + C [/tex]

I combine the constants of integration... i can do this right?

Then i get rid of the log by taking the exponent of both sides.

[tex] P/(M - P) = e^{mkt + c} [/tex]

I then turn [tex] e^{c}[/tex] into [tex] P_{0} [/tex]

Next i divide through by [tex] (M - P) [/tex]

[tex] P = (M - P)P_{0}e^{mkt} [/tex]

next i combine the [tex] P [/tex] then divide through by the remainder.

[tex] P = (mP_{0}e^{mkt})/(1 + P_{0}e^{mkt}) [/tex]

and i end up with:

[tex] P = (mP_{0})/(e^{-mkt} + P_{0}) [/tex]

In the equation i am suppose to get i dont see how there could possibly be three terms in the denominator.

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# Homework Help: DE solve?

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