Is this differential exact or not?

  • Thread starter jenzao
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  • #1
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Homework Statement


Is the differential 3x^2y^3dx+3x^3y^2dy exact or not?
Please show me how to do this problem using Euler's criterion.

Homework Equations





The Attempt at a Solution


Euler says if partial deriv of first term = partial deriv of 2nd term then it must be exact right?
 

Answers and Replies

  • #2
nrqed
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Homework Statement


Is the differential 3x^2y^3dx+3x^3y^2dy exact or not?
Please show me how to do this problem using Euler's criterion.

Homework Equations





The Attempt at a Solution


Euler says if partial deriv of first term = partial deriv of 2nd term then it must be exact right?

To be exact; the partial derivative with respect to y of the first term (the one proportional to dx) must be equal to the partial derivative with respect to x of the second term.
 
  • #3
Defennder
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Yes it appears to be exact. Now all you need to do is to find the potential function.
 
  • #4
HallsofIvy
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Or, more mathematically, find the anti-derivative. "Potential function" is physics terminology.
 

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