Unknown variable within an equation

Hello,

I have an equation of the form P*dawson(sqrt(log(P)-log(A)))== sqrt(B)*T to be solved.

Variable A and B are scalar, but variable T is a vector. I need to solve for P in the equation.

This is the code I have written

syms P
T=5:5:500;
A=2;
B=0.5;
eqn = P*dawson(sqrt(log(P)-log(A)))== sqrt(B).*T ;
s = solve(eqn,P)

    s =

Empty sym: 0-by-1

That is the solution for s I got.

Please advise what can be done.

Thanks.

Answer 1

[Star Strider]

Try this:

syms P T 
A=2;
B=0.5;
eqn = P*dawson(sqrt(log(P)-log(A))) - sqrt(B).*T ;                  % Rearrange
eqnfcn = matlabFunction(eqn, 'Vars',{P,T})                          % Anonymous Function
T=5:5:500;
for k1 = 1:numel(T)
    Pv(k1) = fsolve(@(P)eqnfcn(P,T(k1)), 10);
end

figure
plot(T, Pv)
grid
xlabel('T')
ylabel('P')

Answer 2

[Image Analyst]

dawson needs to be defined also.

[Image Analyst]

Olufemi's "Answer" moved here:

@Image analyst, sorry I don't get what you mean by Dawson needs to be defined. Dawson is a function in MATLAB. For example, you can have dawson(2) = 3.013403889237920e-01 when solved.

Thank you for the response.

[Image Analyst]

OK, it wasn't in my help. It must be in a toolbox that you have that I don't have.

Answer 3

[Walter Roberson]

syms P
T=5:5:500;
A=2;
B=0.5;
s = arrayfun( @(t) vpasolve(P*dawson(sqrt(log(P)-log(sym(A))))== sqrt(sym(B)).*t, P), T);
plot(T, s)

You have to loop solving one value at a time. With the code you had, you were trying to find a single value for P that satisfied all of the equations at the same time.

[Shozeal]

Thanks, Walter.

But I got this error

Error using arrayfun
sym output type is not supported. Set 'UniformOutput' to false.
Error in SystemBeamtest (line 48)
s = arrayfun( @(T) vpasolve(P*dawson(sqrt(log(P)-log(sym(A))))== sqrt(sym(B)).*T, P), T);

I don't know if you interchanged t and T by error or that is how it should be.

[Walter Roberson]

You should not have changed the t to T on the line.

You appear to be using R2015a or earlier (I think it was... I would need to check), as a few releases ago arrayfun() started being able to handle sym variables.

syms P
T=5:5:500;
A=2;
B=0.5;
scell = arrayfun( @(t) vpasolve(P*dawson(sqrt(log(P)-log(sym(A))))== sqrt(sym(B)).*t, P), T, 'uniform', 0);
s = double([scell{:}]);
plot(T, s)

Nearly a straight line.

[Shozeal]

Hi Walter, I actually use R2017a. So, after keeping the t and T in the expression as written above, I got something close to a straight line too. Though it takes a very long time to run if I should increase the range of T.

Thanks.