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:
My(xy)= , and Nx(xy)= .
If the equation is not exact, enter not exact, otherwise enter in F(xy) =
The Attempt at a Solution
I partially differentiated 1xy2-2y and 1x2y−2x to get My and Nx 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!
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