satisfy a solution of an equation

Discussion in 'Differential Equations' started by Dolphin2022, Jun 21, 2022.

  1. Dolphin2022

    Dolphin2022

    Joined:
    Jun 21, 2022
    Messages:
    1
    Likes Received:
    0
    Hi,
    I have been using the diffusion equation based on Ficks 1st, 2nd law and continuity. It has the form

    dy/dt = D*(d^2y/dx^2) (equation 1)

    where d = partial derivative, D= diffusion coefficient, y= flux. It has the solution:

    y(x,t)=1/sqrt(4piDt)*exp^[-x^2/4Dt] (equation 2)

    If you plot this it is a decaying curve such that y-->0 as x-->infinity. Its not too difficult to show that equation 2 satisfies equation 1.

    The thing is, i'm using a growth version of this equation, which has a positive in the exponential of the form

    y(x,t)=1/sqrt(4piDt)*exp^[+x^2/4Dt] (equation 3)

    If you plot this it is a growth curve such that y-->infinity as x-->infinity. But when I try to go through the proof and show that equation 3 also satisfies equation 1 its not quite the same. It may just be I have a minus missing somewhere. If I could get any help on this it would be really great. I just want to know if equation 3 satisfies equation 1?

    thanks
     
    Dolphin2022, Jun 21, 2022
    #1
    1. Advertisements

  2. Dolphin2022

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,758
    Likes Received:
    2,669
    this is what I found for you and think it might be helpful:

    Note that the integral of any function f(x) between x and x +dx is simply f(x) dx!

    upload_2022-6-21_15-2-25.jpeg
     
    MathLover1, Jun 21, 2022
    #2
    1. Advertisements

Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.