Register to reply

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

by fehwqjkfdehqa
Tags: 2y2y, determine, equation, exact
Share this thread:
Jul20-08, 08:16 PM
P: 1
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 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.
Phys.Org News Partner Science news on
Climate change increases risk of crop slowdown in next 20 years
Researcher part of team studying ways to better predict intensity of hurricanes
New molecule puts scientists a step closer to understanding hydrogen storage
Jul20-08, 10:24 PM
P: 136
It is common practice to write it as


and then to differentiate N with respect to x and M with respect to y to check if the equation is exact. The whole method depends on the fact that there is some function where,

[tex] \frac{\partial \Phi}{\partial x}=M(x,y),\text{ }\frac{\partial \Phi}{\partial y}=N(x,y)[/tex]

You can't switch the respectful variables and have it still work so I think you found a special case. For example,


[tex]M_y=2y, N_x=2y[/tex]

so it is exact, but the other way around you get,

[tex]M_x=-2, N_y=2x[/tex]

Hope that helps.

Register to reply

Related Discussions
Differential Equation Exact Solution Calculus & Beyond Homework 2
What do you do if your exact equation isn't exact? and they give u an Integrating F Calculus & Beyond Homework 2
Exact Equation - theory Introductory Physics Homework 5
Exact equation? Introductory Physics Homework 5
An Exact Equation Differential Equations 4