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Simple looking 1st order ode

  1. Oct 7, 2009 #1
    Hello people

    I am an engineer and therefore not a great mathematician.

    To solve a problem involving laminar flow i need to solve the equation with a general form

    dp/dx + A/p - B = 0 which I don't know how to do.

    Can anyone shed any light on how to solve this simple looking problem.

    Many thanks

    Jerome
     
  2. jcsd
  3. Oct 7, 2009 #2

    CompuChip

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    For B = 0 the solution can be written as
    [tex]p^2 = - 2 A x + c[/tex]

    For B not equal to 0, Mathematica gives something with a ProductLog, so there is probably no nice solution, except for special values of A and B.
     
  4. Oct 7, 2009 #3
    Seperation of variables gives you the implicit solution

    p+(A/B)ln(Bp-A)=Bx + constant.
     
  5. Oct 7, 2009 #4
    Dear Defunc

    Many thanks for your reply. I'd be very grateful if you could explain to me how you got the solution. I could not see how to separate variables because of the constant term B.

    Many thanks

    Jerome
     
  6. Oct 7, 2009 #5
    You can seperate it to obtain te following:


    p/(Bp-A) dp=dx.
     
  7. Oct 8, 2009 #6
    thanks, that has helped me a lot!!!
     
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