# Solving an exact differential equation

My work is an attached photo.

I'm trying to solve this differential equation by making it exact (finding an integrating factor etc.) I've been looking at this problem for a few hours now and I can't figure out what it is that I'm doing wrong! The partial derivatives of M(x,y) and N(x,y) that I end up with after multiplying by the integration factor are not equal. Can anyone spot my error?

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Mark44
Mentor
How about posting your work so that we can see it without having to tilt our heads 90 degrees?

How about posting your work so that we can see it without having to tilt our heads 90 degrees?

This should work.

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rock.freak667
Homework Helper
Your integrating factor calculation is correct. When I differentiated your expression (including the integrating factors) I get them to be the same thing. Your calculation of the final differentials are incorrect...at least to me anyhow.

Your integrating factor calculation is correct. When I differentiated your expression (including the integrating factors) I get them to be the same thing. Your calculation of the final differentials are incorrect...at least to me anyhow.

I don't see how they could possible be the same. When you differentiate M with respect to y (using the product rule) you get a y2 in your answer. However when you differentiate N with respect to x you get only a y and not a y2 in your answer. I've used my symbolic calculator to check my differentiation also and I get the same answer.

I still can't see what it is that I'm screwing up here!

anyone?

LCKurtz
Homework Helper
Gold Member
Your M in the denominator testing for mu is missing a factor of y. You should come up with an integrating factor of ey.

Thank you! I knew it must have been something stupid that I wasn't seeing.