Using solve function to find the roots
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syms x
y = 2*x*exp(-x)-sin(x)==0;
d=solve(y,x)
It gives the "zero" as the only value that makes the y zero. But the roots should be 0.8030 and 2.7923 (I have looked from ezplot). Why can't I find the roots with the solve function?
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Walter Roberson
le 18 Jan 2016
solve() can only find all solutions for polynomials. For non-linear functions, it will give a warning and find one numeric solution.
Since you need to switch to numeric solutions anyhow, use vpasolve() with initial guesses to select the range to find the solution over. vpasolve() will only find one solution at a time, but it will allow you to select the range to look in.
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Walter Roberson
le 18 Jan 2016
Looks plausible, except that I would use
y = (log(1+x)+x.^2/2)./(1+x).^2
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