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# EXACT Differential Equation

Posted on 2004-10-02
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Exact Differential Equations:

2y^2-9xy+(3xy-6x^2)y'=0

m=2y^2-9xy   n=3xy-6x^2

partial m, respect to y = 4y-9x

partial n, respect to x = 3y-12x

They are not EXACT.  How do I make this Exact?
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Question by:940775
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Assisted Solution

aburr earned 25 total points
ID: 12208920
you can not (in general)
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Expert Comment

ID: 12208969
change 9 to 12 and 3 to 4
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Author Comment

ID: 12209075
I thought I was to multiply by a number to make it exact
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Accepted Solution

robertjbarker earned 25 total points
ID: 12209251
You want to find a single equation, say f(x,y) such that:

m = df(x,y)/dx = 2y^2-9xy
n = df(x,y)/dy = 3xy-6x^2

If no such function exists, the original equation is not exact.
You can check if an equation is exact if dm/dy is equal to dn/dx.
But if they are not equal, the equation is not exact.
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