Unable to find explicit solution

I tried solving an equation as shown below, and I was constantly getting this error - "Warning: Unable to find explicit solution. For options, see help". I am not able to understand what else to try, I wish to solve for 'y' and I have values for the other parameters, vf, a, x , m and psi predefined. How do I rectify this error?

syms psi x y vf a m
psi = 0.1;
r = 0.3;
a = r; 
m = 1;
x = linspace(-10*r,10*r);
eqn = psi == norm(vf)*(y+m*atan2(y,x+a)-m*atan2(y,x-a));
sol = solve(simplify(eqn),y,'Real', true,'IgnoreAnalyticConstraints', true) ;

[darova]

Did you try vpasolve or fsolve? I think solve can't handle it, it's complicated

Try numerical approach

[Walter Roberson]

vpasolve() cannot handle the situation because vf is not resolved.

Answer 1

[Walter Roberson]

You are trying to solve for a single y value that satisfies all 100 equations simultaneously. That cannot work. You need to solve each of the equations independently:

syms psi x y vf a m
psi = 0.1;
r = 0.3;
a = r; 
m = 1;
x = linspace(-10*r,10*r);
eqn = simplify(psi == norm(vf)*(y+m*atan2(y,x+a)-m*atan2(y,x-a)));
sol = arrayfun(@(EQN) solve(EQN,y,'Real', false,'IgnoreAnalyticConstraints', true), eqn, 'uniform', 0);

... This still will not be able to find the solutions, but that is because there is no solution for general vf