Solve by separation of variables:

dP/dt = P-P^2

This is what I have so far:

P/(P-1)=ce^t

but I need to get that to:

P=(ce^t)/(1+ce^t)

Any help would be greatly appreciated.

Thanks! :)

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- Feb 2nd 2008, 05:35 PMyellowroseDifferential Equations
Solve by separation of variables:

dP/dt = P-P^2

This is what I have so far:

P/(P-1)=ce^t

but I need to get that to:

P=(ce^t)/(1+ce^t)

Any help would be greatly appreciated.

Thanks! :) - Feb 2nd 2008, 05:42 PMJhevon
- Feb 2nd 2008, 06:01 PMyellowrose
- Feb 2nd 2008, 06:12 PMJhevon
oh wait. i made an error. i wrote P(P - 1) when it should have been P(1 - P). that changes things a bit.

......through algerba, or partial fractions if you want to work hard

this is a quadratic in P, use the quadratic formula to solve for P, so:

now simplify ... er, if you can, or want to