Hi there, I am trying to solve a differentiation of long equation. The system shoot me the warning that cannot find a explicit solution. I need the value of X in terms C.

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Vimal 2023-6-1

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https://ww2.mathworks.cn/matlabcentral/answers/1976874-hi-there-i-am-trying-to-solve-a-differentiation-of-long-equation-the-system-shoot-me-the-warning

评论： Walter Roberson 2023-6-2

clc,clear
syms X C
I0=besseli(0,X)
I1=besseli(1,X)
I2=besseli(2,X)
A=(X.*(I1./I0).*((X.^2)-1))+(X.*(I2/I1).*X.^2)
B=(((X.^2)/2).*(I2./I0)).*((2.*((X.^2)-1).*X.^2)-((C./4).^2))
F= 1/2.*((-A) + sqrt((A.^2)-(4.*B)))
Y=diff(F,X)
Y == 0
s=solve(Y)

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Answer 1

John D'Errico 2023-6-1

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I want world peace. Does that mean I can have it? I even need world peace. Still, no good. How about you? You need to solve an equation. The same thing applies. Not every problem has a solution.

In fact, there are infinitely many mathematical problems you can write down that have no solution, and this is surely one of them.

You can use a rootfinder. For example vpasolve or even fzero to find a specific solution for any specific numeric value of C. It may work. It will not find all solutions, since there are likely multiple solutions. But based on your starting value, it should work. However that does not give you a simple formulaic solution, for x as a function of C, and very likely, that is simply not possible.

(Note: In your code, the line Y==0, on its own does NOTHING, except waste CPU cycles.)