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.

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)

Answer 1

[John D'Errico]

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.)

[Vimal]

Thank you so much for your reply, John. I am very new to Matlab and still in the ealry stages of learning. Thank you for your note as well.

[Walter Roberson]

Interestingly you can solve for C in terms of X which is the opposite of what you want.