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

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]

Fist solve the equation for x and then substitue y and then plot.

Answer 1

[Walter Roberson]

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]

Perhaps you have confused the role of x and y, and perhaps you want

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);
x = [1:0.5:30].';
y = zeros(size(x));
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 = 59×1

1.0e+04 * 5.0353 2.7619 1.8483 1.3716 1.0835 0.8923 0.7568 0.6562 0.5787 0.5172

[Walter Roberson]

But there is another possibility: that your y values are given, and you need to calculate 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);
syms x
y = [1:0.5:30].';
X = zeros(size(y));
n=(30-1)/0.5;
for i=1:(n+1)
    eqn = y(i)==52.4*T*((1./x)+(C./(x)^2));
    sol = vpasolve(eqn);
    X(i) = max(sol);
end
plot(y, X)

[lvenG]

Yes, the data set given is for y... so x shall be calculated implicitly... Now I know I should put solve functions for operations of this kind. Really thankful for your help. :)

[Walter Roberson]

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