From what I have heard this exercise should be easy, but I do not know how to resolve it .

Any ideas?

You have two functions, f(x,y) and g(x,y) which satisfy properties:

df/dx = dg/dy and df/dy = - dg/dx.

Show that,

(d^2f)/(dx^2) + (d^2f)/(dy^2) = 0

and

(d^2g)/(dx^2)+(d^2g)/(dx^2) = 0

Thanks!