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Using substiution of the form v=1/y^k to solve 1st order DE

  1. Nov 15, 2009 #1
    [tex]xy'+3y+4y^3=0[/tex]
    use substitution of the form [tex]v=1/y^k[/tex] for some positive integer k. Choose a value of k that cancels the y^3 term.
     
  2. jcsd
  3. Nov 16, 2009 #2

    HallsofIvy

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    Well, have you tried at all? There's not a whole lot of deep thinking involved! Just do exactly what they tell you to do. If [tex]v= 1/y^k[/itex], then [itex]y= 1/v^{1/k}[/itex]. Find the derivative of y and plug it and y into the equation. There should be a single value of k that simplifies the equation.
     
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