Anyways, you need to find a function . Such that,
We need that,
Solving the first (partial) differencial equation we have,
Thus, is partial derivative along is,
But the second equation tells us,
Thus, solving the (partial) differencial equation,
Important, note that after you integrate along y (to solve the differencial equation) you end up with a function of two variables involving x and z (because it is as a constant). But over here you do not because there is no x term on the left, thus it is zero.
We need to solve for .
We still did not yet use equation #3.
Differenciating along z we have,
But the problem says that,
Integrate along z,
Important, note like before usually when you integrate by a certain variable you end up with a multivarible term that places the role of a constant. But in this case everything is one variable so it can only be a constant.