How do I write matlab code for solving the following equation ?

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pawan
pawan on 22 Apr 2014
Answered: Image Analyst on 22 Apr 2014
As we have been provided the y in terms of vector. How can we solve the vector x for corresponding values of y? Please help.
y=0:1:10;
y=x-sin(x)/sqrt(1+sin(x));

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Answers (2)

Mischa Kim
Mischa Kim on 22 Apr 2014
Edited: Mischa Kim on 22 Apr 2014
Pawan, you could do
syms x
y = 0:1:10;
for n = 1:numel(y)
yn(n) = vpasolve(y(n)-x+sin(x)./sqrt(1+sin(x))==0);
end
Note, that there are numerous solutions for a particular y-value.
  2 Comments
pawan
pawan on 22 Apr 2014
Edited: pawan on 22 Apr 2014
Thanks Mischa. But could you do without having symbolic function by assuming any initial value of x say ,0.0001
Mischa Kim
Mischa Kim on 22 Apr 2014
Sure, again, there are multiple solutions, which you will find depending on the starting value.
y = 0:1:10;
for n = 1:numel(y)
yn(n) = fsolve(@(x) y(n)-x+sin(x)/sqrt(1+sin(x)), 10);
end

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Image Analyst
Image Analyst on 22 Apr 2014
If you want to do it numerically, how about
x=0:1:10;
y=x-sin(x)/sqrt(1+sin(x))
plot(x, y, 'bs-', 'LineWidth', 2);
% Try to find x for which y = 5.
desiredY = 5;
[minDiff, desiredXIndex] = min(abs(y - desiredY))
hold on;
plot(x(desiredXIndex), y(desiredXIndex), ...
'r*', 'MarkerSize', 15, 'LineWidth', 2);
grid on;

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