MATLAB: I WANT TO SOLVE THE EQUATION for x: x*exp(x)=(a1-x)*a2*a3 . Here a1 and a3 are matrices and a2 is a constant. I cant solve the equation using solve

Question

sigma=25;
 k=8.61*10^(-5);
 T=linspace(100,500);
E0=1.025;
Ea=E0+0.044;
 t1=1;
 t2=40;
 a1=(sigma./(k.*T)).^2;
 a2=(t1/t2);
a3=exp((Ea-E0)./(k.*T));

This is the code for the problem

Answer 1

True, indeed.

Not only for (A,B) = (11,13) and (3,-6), but for a wide range of other set, including the given coefficients.. I got confused, and enthusiastic, with the closed-form solution.

Thanks Walter, I'm appreciated :)

@Dip Samajdar,

then, as a complement, please check the code below for your problem:

   clc
   clear 
   sigma=25;
   k=8.61*10^(-5);
   T=linspace(100,500);
   E0=1.025;
   Ea=E0+0.044;
   t1=1;
   t2=40;
   a1=(sigma./(k.*T)).^2;
   a2=(t1/t2);
   a3=exp((Ea-E0)./(k.*T));
   syms x 
   A=a1.*a2.*a3;
   B=a2*a3;
      for i=1:numel(A)
          i
          y=x*exp(x) - A(i) + B(i)*x;
          OutPut1(i)=solve(y);
      end
    clc
    disp('The solution is, in a matrix form, ');
    OutPut=double(OutPut1)

This I've checked and it works alright, but it might take a minute or two to finish. Regards.