In the problems given for the Constrained Differentials section 42 of the course, I am having difficulty understanding the solution to problem 3. It appears that in wx and wy, z is set to zero for some strange reason despite no further manipulation of wz. Is there a reason for this or is it simply a mistake?

As a note, earlier in the problem a negative sign was neglected in moving (2xy+y^2)dx to the other side of the equation of when taking the differentials of the constraint equation, which would invalidate the solution as given anyway.

Question

In the problems given for the Constrained Differentials section 42 of the course, I am having difficulty understanding the solution to problem 3. It appears that in wx and wy, z is set to zero for some strange reason despite no further manipulation of wz. Is there a reason for this or is it simply a mistake? 

As a note, earlier in the problem a negative sign was neglected in moving (2xy+y^2)dx to the other side of the equation of when taking the differentials of the constraint equation, which would invalidate the solution as given anyway.