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Math Help - Integrating Factor making DE Exact

  1. #1
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    Integrating Factor making DE Exact

    Hello hello!

    I'm having trouble with more homework questions. This time, it's a DE that needs an IF to make it exact. Here it is

    \frac{x}{2} dt + (t + t^{\frac{1}{2}}sinx)dx = 0

    Anyone able to help?
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  2. #2
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    Quote Originally Posted by exphate View Post
    Hello hello!

    I'm having trouble with more homework questions. This time, it's a DE that needs an IF to make it exact. Here it is

    \frac{x}{2} dt + (t + t^{\frac{1}{2}}sinx)dx = 0

    Anyone able to help?
    The integrating factor is

    \mu = \frac{1}{\sqrt{t}},

    although, if you write your ODE as

    \frac{dt}{dx} + \frac{2t}{x} = - \frac{2 \sqrt{t} \sin x}{x}

    the ODE is Bernoulli.
    Last edited by Jester; August 29th 2009 at 06:26 AM. Reason: additional comment
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