In the course of studying heat conduction, we will always encounter the solution of eigenvalues. When it comes to Bessel functions, I try to solve the eigenvalues with matlab. But it prompts "Cannot find explicit solution" or "Cannot solve symbolically. Returning a numeric approximation instead."
Attached below is the equation I want to solve and my code：
syms n r Beta Lambda ;eqn=n/r*besselj(n,Beta*r)-Beta*besselj(n+1,Beta*r)+Lambda*besselj(n,Beta*r)==0;[solx,params,conds]=solve(eqn,Beta,'IgnoreAnalyticConstraints',1,'ReturnConditions', true);pretty(solx);
I don't know if there is no analytical solution to this problem. If there is no analytical solution, how to deal with such a problem? I would appreciate it if you have good suggestions.