MATLAB: I need to solve an equation involving squares and cubes.

MATLABsolving equations

I need to sole this equation for L, and I have a set of values for d and p.
p = -2(d/L)^3 + 3(d/L)^2
Im wondering how to put this into Matlab. Any help would be apprecitated.

Best Answer

It is a 3rd order equation, it has only an analytical solution.
You can use the following code:
clc; clearvars; 
 
 syms p d L
 
 p=1;
 d=3;
 
 eq= p == -2*(d/L)^3 + 3*(d/L)^2
 
 % analytical solution

 solve(eq,L)
 
 %numerical solution

 vpasolve(eq)
And in case you want to run this for a set of values , you can do the following:
 clc; clearvars;
syms p d L
% values for p, d
pValues=50:10:90;
dValues=300:50:600;
% an empty buffer for the solutions, combined with p,d
SolBuffer=cell(length(pValues)*length(dValues),3);
% solution counter
k=0;
for n=1:length(pValues)
    for m=1:length(dValues)      
        k=k+1;
        
        p=pValues(n);
        SolBuffer{k,1}=p;
        
        d=dValues(m);
        SolBuffer{k,2}=d;
        
        eq= p == -2*(d/L)^3 + 3*(d/L)^2;
        
        % analytical solution
        solve(eq, L);
        
        %numerical solution
        SolBuffer{k,3}=vpasolve(eq).';
        
    end
end
% An example: the third solution
disp('data p and d :')
disp(SolBuffer{3,1})
disp(SolBuffer{3,2})
disp('solutions:')
disp(SolBuffer{3,3})
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