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Can this dsolve code find solution recursively

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MINATI PATRA
MINATI PATRA on 20 Oct 2020
Closed: MATLAB Answer Bot on 20 Aug 2021
syms x f f0(x) f1(x) f2(x) f3(x) f4(x) f5(x) f6(x)
eqn0 = diff(f1,3) == 0; cond0 = [f1(0) == 0, subs(diff(f1),0) == 0, subs(diff(f1),5) == 1 ];
f1 = dsolve(eqn0,cond0);
for m = 2:6
syms f_m
for k = 1:(m-1)
Df = diff(f); D2f = diff(Df); D3f = diff(D2f);
eqn(k) = D3f + (1/2)* f * D2f == 0;
cond(k) = [subs(f,0) == 0, subs(Df,0) == 0, subs(Df,5) == 0];
F = dsolve(eqn(k),cond(k)); f(k) = F.f(k)
end
end
disp([f2 f5 f])
%% I need (f1) to include in the loop to carry the solution and Please help me to run the code.
N.B: Two boundary conditions are different
PLEASE FOLLOW the attached pdf

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