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Math Help - Differential equation

  1. #1
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    Differential equation

    I need to show that this diff eq (x+3x^3siny)dx+x^4cosy\ dy=0 is not exact and multiply it by  \frac{1}{x} to make it exact..

    thanks
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  2. #2
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    Quote Originally Posted by ashes View Post
    I need to show that this diff eq (x+3x^3siny)dx+x^4cosy\ dy=0 is not exact and multiply it by  \frac{1}{x} to make it exact..

    thanks
    So where are you stuck? What working can you show?
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  3. #3
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    reply

    for 1st part i partial diff it wrt y to get 3x^3cosy and 2nd part wrt x to get 4x^3cosy...
    thereafter, do I need to multiply it by x throughout to make it exact?and the general solution is just solving it like a separable diff eq right?
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  4. #4
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    Quote Originally Posted by ashes View Post
    for 1st part i partial diff it wrt y to get 3x^3cosy and 2nd part wrt x to get 4x^3cosy...
    thereafter, do I need to multiply it by x throughout to make it exact?and the general solution is just solving it like a separable diff eq right?
    So you've shown it's not exact. Now you do what the quesiton tells you to do amd multiply through by 1/x (check that this makes it exact). Now solve in the usual way.
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