# Error in plotting an equation given y data sets (y vs x)

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lvenG on 20 Sep 2021
Commented: Walter Roberson on 20 Sep 2021
Hello. I am having trouble plotting a curve y vs x, given y data set from 1 to 30 with an interval of 0.5, through a given equation of
y=52.4*T*((1./x)+(C./(x)^2)); where T and C are constants
The error I am getting is because of the 'sym' that I cannot seem to understand. Please see my code below. Hoping for some help and assistance here. Thank you so much.
syms y x
T=450;
sigma=58.7;
lambda=32.9;
sigma_n=32.3;
lambda_n=7.5;
A=8.314*lambda+sigma/2;
B=32.4*lambda_n+sigma_n/2;
C=sqrt(A*B)/(lambda*lambda_n);
y=[1:0.5:30];
n=(30-1)/0.5;
for i=1:(n+1)
y(i)=52.4*T*((1./x(i))+(C./(x(i))^2));
end
Unable to perform assignment because value of type 'sym' is not convertible to 'double'.

Caused by:
Error using symengine
Unable to convert expression containing symbolic variables into double array. Apply 'subs' function first to substitute values for variables.
plot(x,y);
KSSV on 20 Sep 2021
Fist solve the equation for x and then substitue y and then plot.

Walter Roberson on 20 Sep 2021
Your code wants to calculate the formula for each y value, for all possible x values. But to do that, you have to make the symbolic variable x into a vector of symbolic variables the same size as your vector y.
T=450;
sigma=58.7;
lambda=32.9;
sigma_n=32.3;
lambda_n=7.5;
A=8.314*lambda+sigma/2;
B=32.4*lambda_n+sigma_n/2;
C=sqrt(A*B)/(lambda*lambda_n);
y = sym([1:0.5:30]).';
x = sym('x', size(y));
n=(30-1)/0.5;
for i=1:(n+1)
y(i)=52.4*T*((1./x(i))+(C./(x(i))^2));
end
y
y = Walter Roberson on 20 Sep 2021
In this particular case there is a closed form formula that you can use to calculate the general form, after which you can put in specific y values, instead of having to loop finding the values one by one.
T=450;
sigma=58.7;
lambda=32.9;
sigma_n=32.3;
lambda_n=7.5;
A=8.314*lambda+sigma/2;
B=32.4*lambda_n+sigma_n/2;
C=sqrt(A*B)/(lambda*lambda_n);
syms x Y positive
eqn = Y == 52.4*T*((1./x)+(C./(x)^2));
solX = solve(eqn, x)
solX = y = [1:0.5:30].';
X = double(subs(solX, Y, y))
X = 59×1
1.0e+04 * 2.3581 1.5721 1.1791 0.9433 0.7861 0.6738 0.5896 0.5241 0.4717 0.4288