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Separable Differential Equation

  • #1
1,047
775

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 (:cry:) 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
 

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,224
947

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 (:cry:) 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 ?
 
  • #3
1,047
775
Yes, you're correct, it's P^2 (Sorry about that). I suppose yes, it's a quadratic. Let me see what happens.
 
  • #4
ehild
Homework Helper
15,395
1,802
So your equation is
[tex]\int{\frac{dp}{p-p^2}dp}=\int{dt}[/tex]

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

ehild
 

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