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Not Understanding This Simplification

  1. Jan 27, 2007 #1
    I feel dumb because I can't see how you get from this:

    [tex]x \frac{dy}{dx}+x^2y+y=0[/tex]

    to this

    [tex]\frac{dy}{dx}+(x+\frac{1}{x})y=0[/tex]

    this is what I would of thought it would be...

    [tex]\frac{dy}{dx}+(x+\frac{y}{x})+\frac{y}{x}=0[/tex]

    no?
     
  2. jcsd
  3. Jan 27, 2007 #2

    cristo

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    Why do you think it should be [tex]\frac{dy}{dx}+(x+\frac{y}{x})+\frac{y}{x}=0[/tex]?

    Divide the original equation by x; what do you get?
     
  4. Jan 27, 2007 #3

    arildno

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    Factorize [itex]x^{2}y+y[/itex] in the simplest manner.
    What do you get?
     
  5. Jan 27, 2007 #4
    you get [tex]\frac{dy}{dx}+(\frac{x^2}{x}+\frac{y}{x})+\frac{y}{x}=0[/tex]

    you get [tex]\frac{x^2}{y}+1[/tex]
     
  6. Jan 27, 2007 #5

    arildno

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    No, you don't.

    What does it mean to FACTORIZE?
     
  7. Jan 27, 2007 #6
    [tex]y(x^2+1)[/tex]

    oh I see now... thanks

    but why are you not dividing the y thats on the most right side of the LHS by x?
     
  8. Jan 27, 2007 #7

    arildno

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    So, you have now your diff.eq in the form:
    [tex]x\frac{dy}{dx}+(x^{2}+1)y=0[/tex]
    Multiply this equation with 1/x; what do you get?
     
  9. Jan 27, 2007 #8
    sorry, I see it now... I'm just really bad at these things...
     
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