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Separable differential equation

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data
    (x + 2y) dy/dx = 1, y(0) = 1


    2. Relevant equations



    3. The attempt at a solution

    Problem is, I can't separate it. This might be a homogenous type? If so, how would I make it into the g(y/x) form.

    Thank you.
     
  2. jcsd
  3. Oct 21, 2009 #2

    Mark44

    Staff: Mentor

    Start with u = y/x, or equivalently, y = ux. From this, find dy/dx.
     
  4. Oct 21, 2009 #3
    Okay, so since you said y = ux, I am thinking that this is a homogenous equation...

    However, if it is a homogeneous equation, before we can plug in y = ux, aren't we suppose to first have the equation in the form of dy/dx = f(x,y), where there exists a function such that f(x,y) is expressed g(y/x).

    Then, AFTEr we can do the y=ux thing. correct me if Im wrong.
     
  5. Oct 21, 2009 #4
    Well, that is because it isn't a separateable equation... It isn't even an ODE. Sure it's right?
     
  6. Oct 21, 2009 #5
    Yeah, copied exactly from textbook.
     
  7. Oct 21, 2009 #6

    Mark44

    Staff: Mentor

    You can write the equation as dy/dx = 1/(x + 2y), where the right side is a function of x and y. I'm just offering a suggested approach based on your first post. It may or may not work.
     
  8. Oct 21, 2009 #7
    Yeah, it is a function of x and y, but I don't think it's in the g(y/x) form.
     
  9. Oct 21, 2009 #8
    To me it seems that you are suggesting a linear trial solution?
     
  10. Oct 21, 2009 #9

    Mark44

    Staff: Mentor

    The OP said he wanted to put this into g(y/x) form, so that made me think of the substitution I suggested. I don't have access to my DE textbooks right now, so I don't have any more ideas on solving this one.
     
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