# Separable Differential Equation

dkotschessaa

## Homework Statement

Solve the given differential equation by separation of variables.

dP/dt = P - P2

## 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

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Homework Helper
Gold Member

## Homework Statement

Solve the given differential equation by separation of variables.

dP/dt = P - P2

## 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
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 ?

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

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