How can I determine if the equation (2x+3) + (2y-2)y' = 0 is exact or not?(adsbygoogle = window.adsbygoogle || []).push({});

Now I know I need to take partial derivatives of certain terms of the equation, and call that M and N right?

1. How do I separate the terms?

2. How do I know which variable gets differentiated?

For example , if I separate it so that its:

partial x: (2x+3) = 2

partial y: (2y-2) = 2

2=2, so its exact.

BUT why can't I go:

partial x (2y-2) = 0

partial y (2x+3) = 0

0=0 so thats also exact.

So how do you determine which term is associated with what you are differentiating with repect to???

Also, why do textbooks use M and N??? Whats the point of using these when we can just say "partial differentiate with repect to x" and "partial differentiate with repect to y"

Also, does M ussually go with x and the N ussually go with y and why?

Please explain this to me my brain is about to explode.

Thanks

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# How can I determine if the equation (2x+3) + (2y-2)y' = 0 is exact or not?

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