MATLAB: Unable to find explicit solution.

explicitMATLABsolution

I'm trying to find a the point where a function have a maximum(Lambda_max), the function is the Planck's law that gives the monochromatic emittance of a blackbody(Mi). So first I try to calculate the derivative of Mi with respect to lambda, and then find where it equals to zero, but I can't find a solution "Unable to find explicit solution." I'm using MATLAB 2017a
clc;clear all;
c=2.997*10.^8;% m/s la vitesse de la lumière dans le vide 
h=6.625*10.^-34;% J.s constante de Planck 
k=1.38*10.^-23;%  J/K constante Boltzmann 
syms lambda 
syms T
Mi=(2*h*c*c./(lambda.^5)).*1./(exp(h.*c./(k.*T.*lambda))-1);
D1=diff(Mi)/lambda
solx1 = solve(D1==0 , lambda, 'IgnoreAnalyticConstraints',true)

Best Answer

solx1 = 1729625326210841/(120214954585829120*T*(lambertw(-5*exp(-5))+5))

your D2 is lambda times larger than D1 (caution: you did not specify the variable of derivation for D1). Because it is just lambda times larger, all non-zero solutions for the two are the same.

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