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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- Sep 28th 2012, 10:01 AMnivek0078exact 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) - Sep 28th 2012, 10:16 AMMarkFLRe: 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:

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

Rewriting the ODE in differential form, we have:

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