# Why do I get empty result?

2 views (last 30 days)
Faezeh Manesh on 4 May 2020
Commented: Faezeh Manesh on 5 May 2020
Hello all,
I have the following equation that needs to be solved by MATLAB but it gives me empty sym. I don't know why
syms T a b
eqn= (a*b*exp(b/T)*((1 - exp(a*b*ei(b/T) - T*a*exp(b/T))*exp(294*a*exp(b/294) - a*b*ei(b/294))) - 1))/T^2 == 0;
solT = solve(eqn,T)
Even when I give values for a and b, MATLAb gives me the same message:
syms T
a=(exp(183.8)/1.5);
b=-6.2662e+04;
eqn= (a*b*exp(b/T)*((1 - exp(a*b*ei(b/T) - T*a*exp(b/T))*exp(294*a*exp(b/294) - a*b*ei(b/294))) - 1))/T^2 == 0;
solT = solve(eqn,T)
I would be thankful if someone help me with this.
Faezeh Manesh on 5 May 2020
Thanks. Then how can I find the peak? My ultimate goal is to find the peak in terms of a and b

Steven Lord on 4 May 2020
When I display the expression in the Live Editor, I see that the numerator of the expression is the product of a (very large) constant positive value and two exponentials. That numerator, divided by T^2, is supposed to be equal to 0.
The constant is positive. The values of the two exponentials are only 0 in the limit; there's no finite value z for which exp(z) is 0.
So MATLAB correctly gave the answer that there is no solution to your equation as written.
Your expression does look a little unusual, though. Did you intend to have the Ei and one of the exponentials inside the exponent of another exponential call? Maybe there's a parenthesis in the wrong place?
Faezeh Manesh on 5 May 2020
Actually what I am trying to do is as follows:
I have a diferential equation which has the following form:
when I solved this (with a and b known) and thenfind dy/dT in terms of T, it becomes a figure like this:
I am trying to find the peak in terms of a and b. So, firstly I solved my differential equation symbollicaly in MATLAB to find y(T), then I differentiate dy/dT once more to find dy2/dT2 in terms of y and T. Then I substituted y(T) which had been obtained previously in it. So, my equation would only be in terms of T and then I want to put it equal to zero to find the peak in terms of a and b. but here I substituted my experimental value for a and b o check my answer. So, all I found is from MATLAB