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(x, y) is the left hand side of the differential equation. that is, level curves f(x, y)=c are solutions to the differential equation
find and and it the equation is exact, find f(x, y) too.

You have partial derivatives




which are not equal, so the equation is not exact.

- - -

In case you meant to write



the equations would be exact, since



and in this case the ODE would be exact. I don't suppose it would hurt to demonstrate how to proceed with solving the ODE...

We're looking for a solution of the form , which means that upon differentiating we have



which is to say that we can find by integrating and .





Differentiating with respect to , we have






Thus the general solution (again, assuming you made a typo) would be



and since both s can be treated as arbitrary constants,