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Determine the general solution of QL PDE

  1. Aug 6, 2011 #1
    1. The problem statement, all variables and given/known data

    1) Determine the general solution of the equation

    2) Use implict differentiation to verify that your solution satisfies the given PDE

    2. Relevant equations

    [tex]u u_x-y u_y=y[/tex]


    3. The attempt at a solution

    [tex]\frac{dx}{u}=\frac{dy}{-y}=\frac{du}{y}[/tex]

    Take the second two

    [tex]\int-dy=\int du \implies u=-y+A[/tex]

    Taking the first two

    [tex]\frac{dx}{(-y+A)}=\frac{dy}{-y} \implies dx=\frac{(-y+A)dy}{-y}[/tex]

    Integrating gives

    [tex]x=y-A \ln(y) + f(A)[/tex] but [tex]f(A)=u+y[/tex] therefore the general solution implicitly is

    [tex]x=y-A \ln(y) + u+y[/tex]


    1) How am I doing?
    2) I dont know how to do second question assuming above is correct
    3) How do I create the tags automatically?

    Thanks
     
    Last edited: Aug 6, 2011
  2. jcsd
  3. Aug 6, 2011 #2
    Last edited by a moderator: Apr 26, 2017
  4. Aug 7, 2011 #3
    I realised I left out the function f symbol as highlighted above. Any ideas?
     
  5. Aug 7, 2011 #4
    This is solved....See link in post 2

    Cheers
     
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