1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: 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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook