How to find the roots of a non-polynomial equation in terms of symbolic variables ?

want to find the values of 'K' for which the function (D) becomes zero. 'L' and 'a' are the constants. Code:

syms A B L K a
D = [cosh(K*L)-cos(K*L), sinh(K*L)-sin(K*L); sinh(K*L)+sin(K*L)+K*a*L*(cosh(K*L)+cos(K*L)), cosh(K*L)-cos(K*L)+K*a*L*(sinh(K*L)+sin(K*L))];
d = det(D)
fzero(@(K) d, 10)

Error using fzero (line 309) Function value at starting guess must be finite and real.

[Denel]

Have you tried different starting values for the fzero() function? The error-message states that your starting value isn't valid, since the function's value in that point (10), is probably infinite or complex.

Answer 1

[Walter Roberson]

The Symbolic toolbox is not able to solve such equations.

syms a A B K L real
D = [cosh(K*L)-cos(K*L), sinh(K*L)-sin(K*L); sinh(K*L)+sin(K*L)+K*a*L*(cosh(K*L)+cos(K*L)), cosh(K*L)-cos(K*L)+K*a*L*(sinh(K*L)+sin(K*L))];
d = det(D)

d = 

solve(d, K)

Warning: Unable to find explicit solution. For options, see help.

 
ans =
 
Empty sym: 0-by-1
 

dexp = rewrite(d, 'exp')

dexp = 

solve(dexp, K)

Warning: Unable to find explicit solution. For options, see help.

 
ans =
 
Empty sym: 0-by-1
 

dexpsimp = simplify(dexp)

dexpsimp = 

solve(dexpsimp, K)

Warning: Unable to find explicit solution. For options, see help.

 
ans =
 
Empty sym: 0-by-1