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Solve numerical equation with Y at both sides

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Ron Nativ
Ron Nativ 2020-8-23
评论： Star Strider 2020-8-24
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

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回答（3 个）

KSSV
KSSV 2020-8-23
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)
Star Strider
Star Strider 2020-8-23
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.
Alan Stevens
Alan Stevens 2020-8-23
编辑：Alan Stevens 2020-8-23
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.

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