Need some change in the present Analytical solution code which I'm unable

syms x F1(x) G1(x) H1(x) n fw h
Nt = 0.5; Nb = 0.5; Pr = 1; Le = 2; DF = diff(F1,x); 
eq1 = diff(F1,x,3) + diff(F1,x,2) == 0; eq2 = diff(G1,x,1) + diff(G1,x,2) == 0; eq3 = diff(H1,x,1) + diff(H1,x,2) == 0; 
EQ = [eq1, eq2, eq3]; S = dsolve(EQ);f1 = S.F1;  
F(1) = fw + 1 - exp(-x); 
for m = 2:5
    for k = 1:m-1
        K = F(k)*diff(F(m-k),2) - (2*n/(n+1))*diff(F(k))*diff(F(m-k));
        F(m) =  f1 + F(m-1) + h*( diff(F(m-1),3) + int(int(int(K))) + int(int(K)) );
    end
end
F = F(1)+F(2);F0 = subs(F,x,0); dF0 = subs(diff(F,x),x,0); dFI = subs(diff(F,x),x,Inf);  
sv = solve(F, {F0 == fw, dF0 == 0,dFI == 0}) 

%% I want to simplify 'F' by putting the conditions {F0 == fw, dF0 == 0,dFI == 0}, so that the values of the Constants present in 'F' can be find out.

[P.K. Pattnaik]

@ Thanks Torsten

Can it be possible for you to import some of your ideas.

[P.K. Pattnaik]

Can somebody help here

[Walter Roberson]

use subs() to do the replacements before solving.

subs(F, {list of things to replace}, {list of things to replace with})

Answer 1

[Torsten]

syms x F1(x) G1(x) H1(x) n fw h
Nt = 0.5; Nb = 0.5; Pr = 1; Le = 2; DF = diff(F1,x); 
eq1 = diff(F1,x,3) + diff(F1,x,2) == 0; eq2 = diff(G1,x,1) + diff(G1,x,2) == 0; eq3 = diff(H1,x,1) + diff(H1,x,2) == 0; 
EQ = [eq1, eq2, eq3]; S = dsolve(EQ);f1 = S.F1;  
F(1) = fw + 1 - exp(-x); 
for m = 2:5
    for k = 1:m-1
        K = F(k)*diff(F(m-k),2) - (2*n/(n+1))*diff(F(k))*diff(F(m-k));
        F(m) =  f1 + F(m-1) + h*( diff(F(m-1),3) + int(int(int(K))) + int(int(K)) );
    end
end
F = F(1)+F(2);
F0 = subs(F,x,0);
dF0 = subs(diff(F,x),x,0);
dFI = subs(diff(F,x),x,Inf);  
var = symvar(F)

var = 

C1 = var(1);
C4 = var(2);
C5 = var(3); 
sol = solve([F0==fw,dF0==0,dFI==0],[C1 C4 C5]);
F = simplify(subs(F,[C1 C4 C5],[sol.C1,sol.C4,sol.C5]))

F = 

[MINATI PATRA]

But it is not working if we take

F = F(1)+F(2)+F(3)+F(4)+F(5);

instead of

F = F(1)+F(2);

[Torsten]

Yes, F'(Inf) = NaN if F = F(1)+F(2)+F(3)+F(4)+F(5)

But this is problem-immanent - MATLAB cannot change the mathematics of the problem.

[P.K. Pattnaik]

ok