What to take as p(x,y) and q(x,y) with partials

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SUMMARY

The discussion focuses on determining the exactness of a differential equation represented as P(x,y)dx + Q(x,y)dy = 0. The equation is confirmed to be exact if the condition ∂P/∂y = ∂Q/∂x holds true. In this case, P(x,y) is defined as 5x + 4y, leading to ∂P/∂y = 4, while Q(x,y) is defined as 4x - 8y², resulting in ∂Q/∂x = 4. Both partial derivatives are equal, confirming the equation's exactness.

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Your DE is P(x,y)dx + Q(x,y)dy = 0 and you want to find out if it is exact.

The equation will be exact if [tex]\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x}[/tex].

You have P(x,y) = 5x + 4y giving [tex]\frac{\partial P}{\partial y}=4[/tex]

And Q(x,y) = 4x - 8y² giving [tex]\frac{\partial Q}{\partial x} = 4[/tex]

Have a look at http://www.sosmath.com/diffeq/first/exact/exact.html" and see if it helps.
 
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Great, I took a quick glance at the sight and it looks as if that will help a lot. I will have to take a deeper look into it later this afternoon, but I just wanted to say thanks for your imput. I'll let you know if I have any more problems. =p

thanks! ^_^
 

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