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I have a question and just need you to tell me the steps I have to do. I have an equation with boundary conditions.the question is how can I find f(x)? I don't want to use the predefined Matlab.Please just show me the steps I need to solve this problem. Thanks...

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Bahram
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    step 1 - read the chapter on 2nd order eq with boundary conditions https://www.stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/upfiles/3c3-2ndOrderLinearEqns_Stu.pdf – dpdp Jan 14 '21 at 19:24
  • This is a linear DE, so in principle you can find the solution manually, and use Matlab to find the coefficients from the boundary conditions. – Lutz Lehmann Jan 14 '21 at 21:12

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Simply you can use symbolic math toolbox in MATLAB:

syms f(x) % Define symbolic function

F = dsolve(diff(f,2) + diff(f,1) + 200*f == 0); 

% Find C1 and C2 constants 
syms C1 C2 L

BC_eq(1) = subs(F, x, 0) - 0;
BC_eq(2) = subs(F, x, L) - 100;

C_val = solve(BC_eq, [C1, C2]);

% Substitude C' values in F
F_final = subs(F, {C1, C2}, {C_val.C1, C_val.C2})
Mansour Torabi
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