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Non-linear first order ODE

  1. Feb 26, 2015 #1

    joshmccraney

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    1. The problem statement, all variables and given/known data
    $$y' y + \frac{y}{x} = 1 - 2x$$

    2. Relevant equations
    nothing comes to mind

    3. The attempt at a solution
    i've guessed a quadratic but that didn't work. now i'm stuck. any ideas? also, this is not homework, but a problem I am working on.

    Thanks!
     
  2. jcsd
  3. Feb 26, 2015 #2

    BiGyElLoWhAt

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    Is y y(x)?
     
  4. Feb 26, 2015 #3

    joshmccraney

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    sorry, yes, ##y = y(x)##
     
  5. Feb 26, 2015 #4

    LCKurtz

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  6. Feb 26, 2015 #5

    joshmccraney

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    This is an interesting website. When I perform their substitutions I arrive at $$y \frac{dy}{dz} -y = \frac{2x - 1}{\ln | x |} : z:= \int -\frac{1}{x} dx$$ but from here their table provides no further help. Do you suppose this problem has never been analytically solved?
     
  7. Feb 26, 2015 #6

    LCKurtz

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    I have no idea but it wouldn't surprise me.
     
  8. Feb 27, 2015 #7

    BiGyElLoWhAt

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    This did appear deceptively easy at first glance =/
     
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