Partial differential question:is it right or wrong question,please solve?

Question

If Z=x+y+f(x,y)

where f(x,y) is an arbitrary function of "x" and "y".Obtain the partial differential equation and identify whether the obtained equation is linear or non linear.

Answer 1

What is the significance of "Z"?  You have not provided sufficient information to answer the question. Where would the differential equation be coming from?  What field of study is this?

How about providing a few hints as to the context of this question?