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Homogeneous substitution DE

  1. Sep 16, 2015 #1
    1. The problem statement, all variables and given/known data
    x(dy/dx) - y = sqrt(xy +x2)


    2. Relevant equations


    3. The attempt at a solution
    I got up to this point: u=y/x

    dy/dx = (sqrt(xy+x2))/x + y/x

    And then the solution shows this:

    dy/dx = y/x + (y/x+1)½

    Please help, I don't understand how they got to that point.
     
  2. jcsd
  3. Sep 16, 2015 #2
    Also, sorry about the bad formatting. Where did they move the square root symbol and fraction symbol?
     
  4. Sep 16, 2015 #3

    epenguin

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    Gold Member

    It's fairly elementary algebra that was probably dinned into you at some point and you have forgotten.

    √(xy + x2)/x = √(xy + x2)/√((x2) = √[(xy + x2)/x2] = ...

    You might last time have lost sight of the why, just drilled to do that: hope something comes back but this time instead look to see how it makes sense.
     
    Last edited: Sep 16, 2015
  5. Sep 16, 2015 #4
    Thank you so much!!! Haha its been a minute since I've had algebra. Great explanation! :D
     
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