Solving for p in Differential Equation - Stephen

  • Context: Undergrad 
  • Thread starter Thread starter StephenDoty
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Discussion Overview

The discussion revolves around solving a differential equation related to population growth, specifically focusing on isolating the variable p in the equation derived from integrating the original differential equation. The conversation includes algebraic manipulations and the application of initial conditions to find constants.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • Stephen presents the equation p = (p - 100)(C2e^(kt)) and seeks help to isolate p.
  • Some participants suggest that showing the original differential equation dp/dt = kp(1 - p/100) would be helpful.
  • One participant critiques Stephen's algebra skills, implying that understanding algebra is necessary for tackling differential equations.
  • Another participant expresses frustration at being belittled for asking questions, emphasizing that they have attempted to solve the problem independently.
  • Participants discuss the need for additional information to determine constants C2 and k, suggesting the use of initial population data from specific years.
  • There is mention of a related thread discussing similar equations, indicating that the topic may have been addressed elsewhere in the forum.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of critiquing algebra skills while discussing differential equations. There is no consensus on the best approach to simplify the equation or on the necessity of algebra proficiency for solving such problems. Additionally, while some agree on the use of initial conditions to find constants, others question the clarity of the algebra involved.

Contextual Notes

Limitations include the lack of clarity on how to simplify the expression -100C2e^(kt)/(1 - C2e^(kt)) and the dependence on specific initial conditions for determining constants. The discussion also reflects varying levels of confidence among participants regarding algebraic skills.

Who May Find This Useful

This discussion may be useful for students working on differential equations, particularly those interested in population dynamics and the application of initial conditions to solve for constants in mathematical models.

StephenDoty
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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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You should show the original equation.
 
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.
 
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).
 
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.
 
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!
 
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 referring to. But, honestly, it doesn't make any difference at all.BTW, if you are referring 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!
 
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.
 
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.
 

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