Is this differential exact or not?

[jenzao]

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?

 

[nrqed]

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.

 

[Defennder]

Yes it appears to be exact. Now all you need to do is to find the potential function.

 

[HallsofIvy]

Or, more mathematically, find the anti-derivative. "Potential function" is physics terminology.