5.39 How to solve a set of equations for differentials?

This is problem 7.15 chapter 4 in Boas:

Given \(x^2 u-y^2 v=1\) and \(x+y=uv\) Find \(\frac {dx}{du},v\) and \(\frac {dx}{du},y\)

This is the maple code to solve this:

restart; 
eq1:=x^2*u-y^2*v=1; 
eq2:=x+y=u*v; 
r1:=D(eq1); 
r2:=D(eq2); 
r1_:=subs(D(v)=0,r1); 
r2_:=subs(D(v)=0,r2); 
sol:=solve({r1_,r2_},{D(x),D(u)}); 
print("dx/du,v="); 
rhs(sol[1])/rhs(sol[2]); 
 
r1_:=subs(D(y)=0,r1); 
r2_:=subs(D(y)=0,r2); 
sol:=solve({r1_,r2_},{D(x),D(u)}); 
print("dx/du,y="); 
 
rhs(sol[1])/rhs(sol[2]);