Solve multiple equations for multipe variables

I have the following problem: I want to solve the equation for b: (12*pi^2*a^4+8*pi^2*a^2*b^2+12*pi^2*b^4)/(3*a^2*b^4) == y

Where a is a constant y N are fixed values, So i give N values of y and i want matlab to return N values for b that solves this equation.'

I have currently done this:

Elastic_prop = E*linspace((f_p/E)*0.5, f_p/E, 5)

n_xx = (12*pi^2*a^4+8*pi^2*a^2*b^2+12*pi^2*b^4)/(3*a^2*b^4);

n_xxv = subs(n_xx, b, sym('b', [1 5]))

n_xxp = solve(n_xxv == Elastic_prop, sym('b', [1 5]))

Can any of you help me with this problem?

Answer 1

[Cesar Antonio Lopez Segura]

Hi Roy,

Tets this code and let me know if you need some help:

a = 4 ;y = 22.5; % Known values
xo = 1; % initial b val
fun = @(b) ( 12*pi^2*a^4 + 8*pi^2*a^2*b^2 + 12*pi^2*b^4 )/( 3*a^2*b^4 ) - y; % fun definition
fzero( fun,xo )

Here the solution:

b = 2.512065597813919

In a general case with 9 y values the code should be:

%%In case of 9 y values
a = 4 ;
y = [ 22.5 8 7 5 4 3 78 21 96 ];% Known values
for i = 1:length(y)
xo = 1;
fun = @(b) ( 12*pi^2*a^4 + 8*pi^2*a^2*b^2 + 12*pi^2*b^4 )/( 3*a^2*b^4 ) - y(i);
b(i)= fzero( fun,xo );
end
b

Command window response:

b =

     2.512065597813919   3.650354401760769   3.880731223730568   4.671356482408150   5.534336598056011   8.191022687818798   1.752511072336621   2.567332724890523   1.656264772243542

[Roy Cornelissen]

Gives the desired result, thank you very much!