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