If you exponentiate the left side, you getP/(P - 1) = Ce^(2t)

[SpartanG345]

Homework Statement

dP/dt = 2P(1-P)
write a explicit expression for the dependent variable

Homework Equations

Seperable equation

The Attempt at a Solution

Is the dependent variable P
does this mean you should write a function of P in terms of t?

separation of variables then integration

lnP - ln(p-1) = 2t + C
p/(P-1) = e^2t + e^c

this is all i can get i cannot get an explicit relationship for the dependent variable which is P
wolfram gave this

http://www.wolframalpha.com/input/?i=dx/dt+=+2x*(1-x)"

i cannot get that no idea totally stuck :(

 

[lanedance]

Homework Statement

dP/dt = 2P(1-P)
write a explicit expression for the dependent variable

Homework Equations

Seperable equation

The Attempt at a Solution

Is the dependent variable P
does this mean you should write a function of P in terms of t?

separation of variables then integration

lnP - ln(p-1) = 2t + C
p/(P-1) = e^2t + e^c

first it doesn't look like you have taken the exponential of the RHS correctly,

second when you have, multply both sides by (p-1), group p terms & divide by the coefficient you get, hopefully should get you closer

this is all i can get i cannot get an explicit relationship for the dependent variable which is P
wolfram gave this

http://www.wolframalpha.com/input/?i=dx/dt+=+2x*(1-x)"

i cannot get that no idea totally stuck :(

 

[Mark44]

lnP - ln(p-1) = 2t + C
p/(P-1) = e^2t + e^c

The step missing in the middle is
ln(P/(P - 1)) = 2t + C

When you exponentiate (make each side the exponent on e), what you ended up with on the right side is incorrect. e^(2t + C) != e^(2t) + e^C