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Substitution to make it seperable

  1. Jul 13, 2009 #1
    [tex]\acute{y}+xy^{3}+\frac{y}{x}=0[/tex]
    [tex]y(1)=2[/tex]
    using substitution [tex]u=y^{-2}[/tex]

    [tex]e^{y}\acute{y}=e^{-x}-e^{y}[/tex]
    [tex]y(0)=0[/tex]
    using substitution [tex]u=e^{y}[/tex]

    i could not make these equations seperable and solve for the IVP.
    Anyone has any idea?

    Edit: these problems are not homework, but for self study for preparation to the midterm.
     
    Last edited: Jul 13, 2009
  2. jcsd
  3. Jul 13, 2009 #2

    rock.freak667

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    Homework Helper

    [tex]\frac{dy}{dx}+xy^{3}+\frac{y}{x}=0 [/tex]

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


    Now read http://en.wikipedia.org/wiki/Bernoulli_differential_equation" [Broken] for the rest really.
     
    Last edited by a moderator: May 4, 2017
  4. Jul 13, 2009 #3
    thank you, I solved them all.
     
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