Solve Equation with symbolic Constants numerically.

Question

Niklas Kurz 2023-6-8

编辑： Torsten 2023-6-8

Say I have got the Planck's law whose maximum I want to determine numerically:

% a = hbar/(pi^2*c^3)
% b = hbar./(kB*T); 
syms w a b positive real; u = a * w^3/(exp(b*w)-1);
du = diff(u,w);

How can I numerically solve du for w but leaving constants a and b?

I tried many solvers like

fzero(matlabFunction(du),w)

But all of these accept constants in the form of double inputs only.

Is there a way to get a result with Constants included? Like:

w = 2.82 * b % this is in fact the standard result.

Answer 1

Torsten 2023-6-8

编辑：Torsten 2023-6-8

syms w a b positive real

u = a * w^3/(exp(b*w)-1);

du = diff(u,w);

wsol = solve(du==0,w)

wsol =