Solving for p in Differential Equation - Stephen

  • Thread starter StephenDoty
  • Start date
In summary, Stephen is asking for help with differential equation, integration, and solving for p. He has tried everything he knows and is stuck. He is not a good person and his intelligence is overestimated.
  • #1
StephenDoty
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0
I am currently working on differential equation. I have integrated both sides and I get:
p/p-100= C2e^(kt)
p= (p-100) * (C2e^(kt))

How do I get p by itself on the left hand side. I need to solve for p.

Thank you.

Stephen
 
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  • #2
You should show the original equation.
 
  • #3
orig

dp/dt = kp(1-p/100)


But all I need to know is how to solve for p in the equation p= (p-100)(C2e^kt).

Thank you.
 
  • #4
I guess it would be naughty of me to say that you shouldn't be doing differential equations if you can't do algebra! (So I won't.)

Starting from p= (p-100) * (C2ekt), multiply out the right side: p= C2ektp- 100C2ekt. Subtract C2ektp from both sides:p- C2ektp= -100C2ekt so p(1- C2ekt)= -100C2ekt. Finally, divide both sides by 1- C2ekt:
p= -100C2ekt/(1- C2ekt).
 
  • #5
HallsofIvy said:
you shouldn't be doing differential equations if you can't do algebra!.

Neither do i understand this. People tend to have elementary problems in differentiating and integrating some really simple looking functions, and they do Diff. Equations.
 
  • #6
I got exactly what you got. I have a very high IQ and am a member of several high IQ groups and I even have a 4.0 at tech. However, the -100C2e^kt/(1- C2e^kt) has to be simplified so I can plug information in for C2 and k and I do not know how to do so. When I ask about anything it means that I have tried everything I know and cannot figure it out or am unsure of my answer. A good teacher and person does not belittle or demean someone for asking a question. SHAME ON YOU!
 
  • #7
StephenDoty said:
I got exactly what you got. I have a very high IQ and am a member of several high IQ groups and I even have a 4.0 at tech. However, the -100C2e^kt/(1- C2e^kt) has to be simplified so I can plug information in for C2 and k and I do not know how to do so. When I ask about anything it means that I have tried everything I know and cannot figure it out or am unsure of my answer. A good teacher and person does not belittle or demean someone for asking a question. SHAME ON YOU!

Well, i do not know who you are reffering to. But, honestly, it doesn't make any difference at all.BTW, if you are reffering to me, i am not a teacher and neither do i tend to be a good person...lol...
Nobody here was trying to belittle, offend, blame,demean, contempt, you, or anything like this. And yes, i agree that every question has its value, but i do now withdraw what i said before: It is ridiculous that people have simple algebra problems while they work on Calculus II, Diff. eq, Lin. Algebra or anything like that. Making your way to those courses, somehow means that you already know what preceeds these subjects. I am not saying these things to you personally, but rather in general, so there is no room to get offended.

StephenDoty said:
SHAME ON YOU!

If you really want to offend people like this, i would suggest find some other place!
 
  • #8
StephenDoty said:
I got exactly what you got. However, the -100C2e^kt/(1- C2e^kt) has to be simplified so I can plug information in for C2 and k and I do not know how to do so. !
Well, if you want to find C2, and k, there have to be some extra information on your original problem.
 
  • #9
there was: in there year 1990 the pop was 5.28billion and in 2000 the pop was 6.07billion
 
  • #10
StephenDoty said:
there was: in there year 1990 the pop was 5.28billion and in 2000 the pop was 6.07billion

Well, now make use of this fact, that is let t=0 correspond to the year 1990, and t=10, correspond to the year 2000. Now assuming that p (on your equation) is the population you have two initial conditions,
p(0)=5.28billion and --> from this one you will be able to find C2
p(10)=6.07billion --> from this one, and also now using the result for C2, you will be able to find k.

From here on, only some simple algebraic steps are included.
I think you'll be fine.
 
Last edited:
  • #11
sutupidmath said:
From here on, only some simple algebraic steps are ncluded.

Solving the original equation for p was also simple in that sense :smile:
 
  • #12
Pere Callahan said:
Solving the original equation for p was also simple in that sense :smile:
Are you suggesting that the op won't be agle to handle this either?

And i do agree with what u said...lol...
 
  • #13
As far as I can see, essentially this same equation is being discussed in another thread.
'Logistic growth, population, limits'.
 
  • #14
epenguin said:
As far as I can see, essentially this same equation is being discussed in another thread.
'Logistic growth, population, limits'.

What link?
 
  • #15
sutupidmath said:
What link?

That's the title and right now it's 9 posts down from here in this forum stupidmath.:smile:
 
  • #16
epenguin said:
That's the title and right now it's 9 posts down from here in this forum stupidmath.:smile:

I don't think it is the exact same question though. And defenitely it is asked by someone else.
 
  • #17
Not same question but same equation just with different numerical constants.
 

What is a differential equation?

A differential equation is an equation that involves an unknown function and its derivatives. It represents the relationship between a function and its rate of change.

How do you solve for p in a differential equation?

The process for solving for p in a differential equation depends on the type of equation and its initial conditions. It typically involves using integration and substitution techniques to isolate the variable p.

What is the importance of solving for p in a differential equation?

Solving for p in a differential equation allows us to understand the behavior and properties of the function p. It also allows us to make predictions and solve real-world problems.

What are the different methods for solving differential equations?

There are several methods for solving differential equations, including separation of variables, the method of undetermined coefficients, and variation of parameters. The appropriate method to use depends on the type and complexity of the equation.

Can differential equations be solved analytically or numerically?

Yes, differential equations can be solved both analytically and numerically. Analytical solutions involve finding an exact expression for the function p, while numerical solutions involve approximating the function using numerical methods such as Euler's method or Runge-Kutta methods.

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