Separable Differential Equation

[dkotschessaa]

Homework Statement

Solve the given differential equation by separation of variables.

Homework Equations

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

 

[SammyS]

Homework Statement

Solve the given differential equation by separation of variables.

Homework Equations

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.

 

[ehild]

So your equation is
$$\int{\frac{dp}{p-p^2}dp}=\int{dt}$$

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

ehild