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Nasty first order ODE

  1. Jan 26, 2008 #1
    1. The problem statement, all variables and given/known data

    This problem is from Blanchard "Differential Equations" Chapter one review, question 32.

    [tex]{\frac {d}{dt}}y \left( t \right) -{\frac {y \left( t \right) {t}^{3}}

    3. The attempt at a solution

    Using an integrating factor yields:

    {\frac {d}{dt}} \sqrt [4]{1+{t}^{4}}y \left( t \right) =2\,\sqrt [4]{1+{t}^{4}}

    This is unworkable...

    Any hints would be greatly appreciated. I suspect that I am overlooking a simple guess.
  2. jcsd
  3. Jan 26, 2008 #2

    Ben Niehoff

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    Science Advisor
    Gold Member

    Yeah, you're making it much harder than it is. Just multiply out by [itex](1+t^4)dt[/itex], and you get

    [tex](1+t^4)dy - yt^3dt = 2(1+t^4)dt[/tex]

    Hint: try to make the left side look like the Quotient Rule. What is the derivative of [itex](1+t^4)[/itex]?
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