solve the question ( fsolve , vpasolve)

is there any other way to solve the equation below.

clear all;clc;


a=0.5;
x=linspace(-2*a,2*a,100);
eqn=@(x,y,a)(y.^2./(x.^2+y.^2)).*(1-2.*(1-(x./(2*a)).^2-(y./(2*a)).^2))-(y./a).^2;
for k = 1:numel(x)
    options = optimoptions('fsolve','Display','iter');
    yv(k,:) = fsolve(@(y)eqn(x(k),y,a), 1, options);
end


plot(x,yv)

when ı change initial value for iteration, answers and graph is changing.

[onur karakurt]

what is the correct y values

[Torsten]

If you multiply your equation by x^2+y^2, you see that you try to solve a quadratic equation in y^2. This equation might have 0, 1, 2 or 4 real solutions. Use symbolic computation using "solve" instead of "fsolve" to sort out the solution that makes sense for your problem.

[Torsten]

Solving your equation by hand gives y=0 as the only solution for all values of a and x different from 0. For x=0, no solution for y exists.

Answer 1

[John D'Errico]

I think you do not understand optimization. When you change the initial value, it is EXPECTED that the solver MAY converge to a different solution.

[onur karakurt]

solve function is not sufficient to answer the question, ı tried this fsolve function. How can I get correct y values.

[onur karakurt]

what is the correct function to solve the equation