1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Separable partial differential equation

  1. May 6, 2015 #1
    1. The problem statement, all variables and given/known data
    I have two equations.
    cos(θ)wφ + sin(θ)wφ = 0 (1)
    And
    ## \frac{w_φ}{r}## + ∂wφ/∂r = 0 (2)
    Find wφ, which is a function of both r and theta.

    2. Relevant equations


    3. The attempt at a solution
    I end up with two equations, having integrated. wφ=## \frac{A}{sinθ}## from (1), and wφ = Ar from (2). A is a constant of integration.
    Is A the same in both equations? How do I combine the two solutions into one? I don't think you add them.
     
  2. jcsd
  3. May 6, 2015 #2
    Have you typed the the first equation correct? Because if not [itex]w_φ=0[/itex], and for the rest: remember that when you differentiate / integrate with respect to [itex]r[/itex] you may have lost a function of θ.
     
  4. May 6, 2015 #3
    I know it isn't zero... But actually the first equation isn't correct, typed wrong.
    Should be sin(θ) multiplied by the partial differential of wφ with respect to theta
     
  5. May 6, 2015 #4
    Did I differentiate instead of integrating? I checked the integration, can't find a mistake.
     
    Last edited: May 6, 2015
  6. May 6, 2015 #5

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    How about writing that first equation again in its corrected form, in its entirety .
     
  7. May 6, 2015 #6
    Sorry. Here it is:
    cos(θ)wφ+sin(θ) ##\frac{∂w_φ}{dθ}=0##.
     
  8. May 6, 2015 #7

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    OK.

    For your question regarding the constant of integration, A .

    You would not expect the two constants of integration to be the same.

    In general, the constant of integration you get by integrating over θ, can be a function of r , etc.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Separable partial differential equation
Loading...