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Math Help - exact ODE

  1. #1
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    exact ODE

    How do i find the M(x,y) and N(x,y) for the form M(x,y) + N(x,y)y'? I'm confused because the x and y values are together do I divide them out. Please show me how.

    Given (dy/dx) = (-x+cos(y)/2+ (x)sin(y)) where y(pi/2)= - (pi/2)
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: exact ODE

    After some contemplation (the over-use of bracketing symbols in some places and the under-use in others made interpretation necessary), I assume you are given the IVP:

    \frac{dy}{dx}=\frac{-x+\cos(y)}{2+x\sin(y)} where y\left(\frac{\pi}{2} \right)=-\frac{\pi}{2}

    Rewriting the ODE in differential form, we have:

    (x-\cos(y))\,dx+(2+x\sin(y))\,dy=0
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