syms x y real
syms delta_x delta_y delta_C real
assume(y >= 0);
assume(delta_x >= -5/100 & delta_x < 5/100);
assume(delta_y >= -5/1000 & delta_y < 5/1000);
assume(delta_C >= -5/1000 & delta_C < 5/1000);
dEv = 25;
dEvbm = x.*(16/10 + delta_x) + y.*(-52/100 + delta_y);
C = 105/100 + delta_C;
V = C .* sqrt(y);
eqn = dEv == (((dEvbm - 1) + sqrt(((dEvbm + 1) .* (dEvbm + 1)) + (4 .* V.*V)))/2);
sol = solve(eqn, x, 'returnconditions', true);
sol.x
sol.conditions
Y = 0.00:0.001:0.08;
X = subs(sol.x, y, Y);
disp(X)
You will get answers similar to
-(delta_C^2/26000 + (21*delta_C)/260000 + delta_y/1000 - 260004967/10400000)/(delta_x + 8/5)
Here, delta_C reflects the undercertainty in the value of C: when you write C = 1.05 then in science that stands in for C being a unknown value that is in the range 1045/1000 (inclusive) and 1055/1000 (exclusive.) It makes no sense to ask for exact solutions to equations that have coefficients that are not exactly known, so I have converted to exact solutions by quantifying the uncertainties.
Does it really make a difference? Yes, it does. For X(2), if you examine over the entire range of uncertainties, the results come out between 15.1518013280886 and 16.1293438703474, which is a quite noticable difference.
I assumed here that dEv = 25 was an exact figure, and that the + 1.0 and - 1.0 were intended to be exact 1's and the 4 multiplying the V^2 was intended to be an exact 4 and the division by 2 was intended to be an exact 2.
