# Making an inexact differential equation exact

1. Oct 9, 2009

### jumbogala

1. The problem statement, all variables and given/known data
I have another question. The following equation is inexact. Find an integrating factor u that makes the equation exact.

(-9/6)x4y6+3x8y7+x6)dx+(−1x5y5+(13/21)x9y6)dy=0

2. Relevant equations
Call the part before dx M, and the part before dy N.

3. The attempt at a solution
We did an example like this in class where to find u we took [(dM/dy)-(dN/dx)] / N. (those are partial derivatives). Then the answer to that was integrated and put to the power of e (e^integrated answer).

I tried doing that but it gave me something weird.

Partial of M with respect to y: -9x4y5 + 21x8y6

Parital of N with respect to x: -5x4y5 + ((21*9)/13)x8y6

Then take the difference between the two and get -4x4y5 -6.46x8y6

And divide that by N. this gives some weird function that I don't think is right because the answers are usually simple. I'm guessing I wasn't supposed to use the same initial formula that the example did, but all the examples seem to use it.

2. Oct 9, 2009

### LCKurtz

The test you are trying is to look for an integrating factor a pure function of x. There is a similar test looking for a pure function of y. You can read about these tests in the thread: