Solving an exact differential equation

[Jimmy25]

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?

 

[Mark44]

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

 

[Jimmy25]

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

This should work.

 

[rock.freak667]

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.

 

[Jimmy25]

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!

 

[Jimmy25]

anyone?

 

[LCKurtz]

Your M in the denominator testing for mu is missing a factor of y. You should come up with an integrating factor of e^y.

 

[Jimmy25]

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