Partial Differential equation problem

[eljose]

let be the function U=U(x,y) satisfying:
$$U_{x}=(a/\epsilon)^{y}y$$ and $$U_{y}=(a/\epsilon)^{x}x$$ (1)
where we have introduced the notation $$U_{i}=dU/di$$ i=x,y then from expression (1) we could construct the differential equation:
$$xU_{x}-yU_{y}=0$$ (2)
from (2) we could construct the solution to obtain U, my problem is how to obtain U so its derivatives respect to x and y give the result in (1)

 

[Tide]

How does (2) follow from (1)?