1. Sep 16, 2005 #1

   Jameson

   

   Find a solution to the following D.E.
   
   [tex]\frac{dy}{dx} + \frac{x}{y}=0[/tex]
   
   [tex]\frac{dy}{dx}=-\frac{x}{y}[/tex]
   
   Separate variables...
   
   [tex]ydy = -xdx[/tex]
   
   Integrate both sides...
   
   [tex]\frac{y^2}{2}=-\frac{x^2}{2}[/tex]
   
   Multiply both sides by 2, and here is where my problem arises...
   
   [tex]y^2=-x^2[/tex]
   
   Stuck. [itex]x^2[/itex] will always be positive, so after applying the negative, I can't take the squareroot. It has to be a simple mistake. Please give a small bit of help or a small hint.

    

   Jameson, Sep 16, 2005
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3. Sep 16, 2005 #2

   Dr Avalanchez

   

   Aaargh... nearly there...
   
   [tex]y^2=-x^2+C[/tex]
   
   Does this ring a bell?

    

   Dr Avalanchez, Sep 16, 2005
4. Sep 18, 2005 #3

   Integral

   

   Staff Emeritus

   Science Advisor

   Gold Member

   Is there some reason you must restrict yourself to the reals? Even with the constant of integration which you need (as above) there is the possibility of a complex solution. A complete problem statement will include the boundary conditions or initial values. You have not provided a complete problem statement. Without that. your solution is complete with the addion of the constant of integration.

    

   Integral, Sep 18, 2005

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