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Help Solving a differential equation

  1. Feb 1, 2006 #1
    Hello, i was wondering if someone can help me along with solving this differential equation.


    (x+2y)y'=y

    I believe you use substitution. Right now I am setting my substitution to
    v=(x+2y), but then when i follow through with my work, it doesn't simplify down to a seperable or first order linear equation. Am I doing something wrong?

    -giuseppe
     
    Last edited: Feb 1, 2006
  2. jcsd
  3. Feb 1, 2006 #2
    try this should make a nice linear in terms of x

    divide the left side by y

    then divide 1 by y' and you should end up with a linear in terms of x
     
  4. Feb 2, 2006 #3
    Rewrite this in the form M(x,y)dx + N(x,y)dy = 0. Then, check if this is an exact differential equation. If not, can you find an integrating factor to make it exact?

    I don't think substitution works here. It's just not separable.
     
  5. Feb 2, 2006 #4

    HallsofIvy

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    This is NOT an exact equation either.

    I like Valhalla's suggestion. You can rewrite it as

    y(dx/dy)= x+ 2y which is a LINEAR equation for x as a function of y. If you really need y as a function of x, invert the function.
     
  6. Feb 2, 2006 #5
    I didn't say it was exact... I said he should check if it was exact. :smile:

    It's easy enough to make it exact with an integrating factor though.

    There is more than one way to skin a cat...
     
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