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Homework Help: Help Check this DE!

  1. Sep 15, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]x^{2}\frac{dy}{dx}-2xy=3y^{4}[/tex]

    2. Relevant equations

    Bernoulli's equation

    3. The attempt at a solution

    [tex]x^{2}\frac{dy}{dx}-2xy=3y^{4}[/tex]

    First I divide through by [tex]x^{2}[/tex] and [tex]y^{n}[/tex] to put it in standard form, and then to begin Bernoulli's equation process.

    [tex]y^{-4}y'-\frac{2}{x}y^{-3}=\frac{3}{x^{2}}[/tex]

    u-substitution:

    [tex]w=y^{1-n}=y^{-3}[/tex]
    [tex]w'=-3y^{-4}y'[/tex]

    Substitute in...
    [tex]\frac{-1}{3}w'-\frac{2}{x}w=\frac{3}{x^{2}}[/tex]

    Put in Standard Form...

    [tex]w'+\frac{6}{x}w=-\frac{9}{x^{2}}[/tex]

    Get the integrating factor...

    [tex]p(x)=\frac{6}{x} \Rightarrow \int\frac{6}{x}dx = 6ln(x)\Rightarrow\mu=e^{6lnx}=x^{6}[/tex]


    [tex]\int\frac{d}{dx}(w*x^{6})dx=\int\frac{-9}{x^{4}}dx[/tex]

    [tex]w=\frac{3}{x^{9}}+cx^{-6}[/tex]

    I'll stop here since I don't think the simplification with help much (w->y^-3)

    Wolfram got this:

    Clickity

    Which kinda-sorta looks like my answer, except the powers are off. Where did I go wrong?

    Using wolfram to simplify, with y^-3 plugged in for w
     
    Last edited: Sep 15, 2010
  2. jcsd
  3. Sep 15, 2010 #2


    That part is wrong.
     
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