The question is asking in other words, does there exists a function .

So that,

We need that,

To see if this if this is possible we can use the "cross-partials test". Or just assume that it is possible and see if we arrive at a result, which is what I am going to do.

The first partial differencial equation solves to:

But that means if we differenciate to respect to y:

So will work for any constant. We can just choose .

Thus, is a function which works.