This would be a function
To recover z we would use partial integration.
so in your example
Now multiplying by dx we get
Now lets take the first part
This is the partial of z with respect to y
Now if we integrate with respect to y we get
where the arbitrary constant is a function of x.
Now we know what the partial of z with respect to x should be so
Now we set this equal to the part above to get
Simplifying we get
Now putting this back into z(x,y) we get