Problem with symbolic variables system

I am confused with symbolic variables and function of a variable.

I have a Y which is a function of D. In fact Y is a vector of size N and each and each Yi=function(D).

I also have a X which is a function of Y. That is Xi=function(Yi) so in the end also X will be a function of D.

Then I have an A=sum(Y*X).

What I need to do is to solve a system of nonlinear equations of dA==0 where da(i)==diff(A,Y(i)) from which I will have as a solution the Y array as a function of D.

I tried this:

N=10;

Y=sym('Y',[1 N]);

X=sym('X',[1 N]);

syms D

A=0;

for i=1:N

      X(i)=sqrt(D^2-Y(i)^2);
      A=A+ Y(i)*X(i); 

end 

dA=sym('dA',[1 N]);

for i=1:N

      dA(i)=diff(A,Y(i));

end

S = solve(dA==0);

But I get this: "Warning: Possibly spurious solutions. [solvelib::checkVectorSolutions]" and it is very slow.

Do you think it is a good way to solve my problem? What is the difference if I define a function dA=myfun(D)?