Assignment: Differential Equation

I have this one question for my Mathematical Modelling unit Assignment 1 which I have been stuck on for hour 8+ hours (deadly serious 0.0).

dP/dt = (1/2)*P(4-P)) P(0) = 2

I try solving it as a separable DE and I get to;

P/(4-P) = A*e^(2t) (Starting to think that this part might be wrong too -.-)

From this point I have tried everything I know to try and solve for P(t)

I REALLYYYYYYY need some help with this one.

Re: Assignment: Differential Equation

Re: Assignment: Differential Equation

Hello, stripe501!

We have: .

Separate variables: .

Partial fractions: .

Integrate: .

. . . . . . . . .

Multiply by 4: . .

. . . . . . . . . . . . . . . . .

Exponentiate: . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .[1]

We are given: . . . when

. .

. .

Substitute into [1]: .

Re: Assignment: Differential Equation

Thanks so much :), you made a few mistakes in the working but that part that I was stuck on had the same method to solve. I got the answer to be P= 4e^(2t)/(1+e^(2t)). Thanks for your help!