Please try to solve this question.
The question is asking in other words, does there exists a function .
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.