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What is the solution of this differential equation?

  1. May 8, 2014 #1
    how can we solve this differential equation?
    (ax+y)∂f/∂x + (ay+x)∂f/∂y =0 with this condition: if a=0 then f(x,y)=x^2 - y^2
     
  2. jcsd
  3. May 8, 2014 #2
    [tex]df=\frac{∂f}{∂x}dx+\frac{∂f}{∂y}dy[/tex]

    At constant f, [tex]\frac{∂f}{∂x}dx+\frac{∂f}{∂y}dy=0[/tex]

    Or equivalently, [tex]\left(\frac{∂y}{∂x}\right)_f=-\frac{(∂f/∂x)}{(∂f/∂y)}[/tex]

    Chet
     
  4. May 9, 2014 #3
    The change of variables (in attachement) leads to a very simple PDE :
     

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