- #1

- 5

- 0

## Homework Statement

Use the "mixed partials" check to see if the following differential equation is exact.

If it is exact find a function F(x,y) whose differential, dF(xy) is the left hand side of the differential equation. That is, level curves F(xy)=C are solutions to the differential equation:

1xy

^{2}−2y)dx+(1x

^{2}y−2x)dy=0

First:

M

_{y}(xy)= , and N

_{x}(xy)= .

If the equation is not exact, enter not exact, otherwise enter in F(xy) =

## Homework Equations

## The Attempt at a Solution

I partially differentiated 1xy

^{2}-2y and 1x

^{2}y−2x to get M

_{y}and N

_{x}respectively. Since they both turned out to be 2xy-2, I concluded that the equation was exact.

At this point, I'm a little lost on what to do. I tried following my notes but I was sick that week in class so I didn't really put coherent/pertinent notes down. Put simply, I'm stuck and super confused. Some websites are telling me to integrate then differentiate, others are telling me just integrate. I'm not sure. I looked at the thread a few days ago that had a very similar problem but could not discern whether the method used was a general solution or a solution for just that problem. Thank you in advance!

Last edited by a moderator: