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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**