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Math Help - Differential Equations General solution help.

  1. #1
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    Differential Equations General solution help.

    how do i get the general solution of:
    dy/dx=(y/(sin(y)-x))


    thanks
    Last edited by mr fantastic; November 5th 2010 at 08:12 PM. Reason: Removed excessive !'s in title.
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  2. #2
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    Hmm. We have

    \dfrac{dy}{dx}=\dfrac{y}{\sin(y)-x}

    \dfrac{dx}{dy}=\dfrac{\sin(y)-x}{y}

    \dfrac{dx}{dy}+\dfrac{x}{y}=\dfrac{\sin(y)}{y}.

    This is first-order linear in x(y).
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  3. #3
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    so the IF is y?

    so you get y*(dx/dy)+x=ysiny
    from that you get: x=(1/y)*siny-cosy
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  4. #4
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    Correct IF. However, the RHS is just sin(y), right? That should simplify things a bit for you.
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  5. #5
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    ah yes i multiplied the if to the rhs! my bad! thanks very much!
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  6. #6
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    You're welcome. Have a good one!
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