Solve numerical equation with Y at both sides

Hi all,

I have a general equation I would like to solve. However, it contains the dependent variable Y on both sides.

The eqaution is: Y/Y_0 = B * (1 + x*Y/D)^0.5 * (1-x)^alpha

Where x is the independent variable,

and Y_0, B, D and alpha are constants. What would be the most appropriate function in Matlab for this particular problem?

Thanks,

Ron

Answer 1

[KSSV]

You can use symbolic package. Something like this:

syms Y_0 Y B x Y D alpha
eqn = Y/Y_0 - B * (1 + x*Y/D)^0.5 * (1-x)^alpha==0 ;
s = solve(eqn,Y)

[Ron Nativ]

Thank you KSSV. Is there a big difference between this and using vpasolve?

Answer 2

[Star Strider]

A numeric approach:

Y_0 = 3;                                                        % Define Constants
B = 5;
D = 7;
alpha = 11;

x = linspace(0, 0.9, 10);

Yfcn = @(Y,x) B * sqrt(1 + x*Y/D) .* (1-x).^alpha - Y/Y_0;      % Use Element-Wise Operations

for k = 1:numel(x)
    Y(k) = fzero(@(Y)Yfcn(Y,x(k)), 0.1);
end

figure
plot(x, Y)
grid

Note that if ‘x>1’ the result will be complex (regardless of what the other constants are), and the fzero function will fail. Consider using fsolve instead in this event.

[Ron Nativ]

Thanks Star Strider. Luckiliy, my x values are always between 0 and 1.

[Star Strider]

Then this should work!

Answer 3

[Alan Stevens]

Your equation can also be expressed as a quadratic in Y

which could be solved using roots (for specified values of x).

You would need to check that the solutions were consistent with the original equation.

[Ron Nativ]

Thanks Alan!