# Separable Differential Equation

1. Sep 6, 2012

### dkotschessaa

1. The problem statement, all variables and given/known data

Solve the given differential equation by separation of variables.

2. Relevant equations

dP/dt = P - P2

3. The attempt at a solution

This is no problem to "solve" except that Webassign () wants to know the whole thing in terms of P.

You end up with

dP/(P-P2) = dt

which is not a difficult integral, but you end up with a left side: (after "e-ing" both sides) of P-P^2. How can I give this in terms of P, or am I thinking wrong? (probably the latter)

-Dave K

2. Sep 6, 2012

### SammyS

Staff Emeritus
I'm assuming that P2 is really P2 .

What is P2 equal to after you integrate?

Don't you have an equation which is quadratic in P ?

3. Sep 7, 2012

### dkotschessaa

Yes, you're correct, it's P^2 (Sorry about that). I suppose yes, it's a quadratic. Let me see what happens.

4. Sep 7, 2012

### ehild

$$\int{\frac{dp}{p-p^2}dp}=\int{dt}$$

Factor out p in the denominator: it becomes a product. You can resolve the LHS integrand to partial fractions.

ehild