F:=f->taylor(f, x, 4);
F(ln(1+x));
F(ln(1+sin(x)));
F(%%-%);
 

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Like before:

A := cos(5*t)=a*cos(t)^5+b*cos(t)^3*sin(t)^2+c*cos(t)*sin(t)^4;
collect(combine((lhs-rhs)(A)), {sin, cos});
solve({coeffs}(%, indets(%, dependent(t))));

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How is this different from this question you asked?
https://www.mapleprimes.com/questions/228216-Question-From-Maple

mul(1/(i+j),j=0..3);
sum(%,i=1..infinity)=1/18;

Try:

plots[pointplot]( [seq([i,S[i]],i=1..numelems(S))], style=line);

You are missing a condition, so it acts like a parameter.

Example:

dsys := {diff(s(x), x, x, x)+(1/2)*s(x)*(diff(s(x), x, x)) = 0, s(0) = 0, (D(s))(5) = 1};
other:=seq({D(s)(0)=i/10}, i=-8..1);;
sol:=seq(dsolve(dsys union cond,numeric), cond=[other]);
plots[display](map(plots[odeplot], [sol], 0..5));

restart;
PDEtools[declare](f(x), prime = x);

N := 4;
F := sum(p^i*f[i](x), i = 0 .. N);
HPMEq := (1 - p)*(diff(F, `$`(x, 3))) + p*((diff(F, `$`(x, 3))) + 1/2*(diff(F, x, x))*F);
for i from 0 to N do equ[2][i] := coeff(HPMEq, p, i) = 0 end do;

cond[1][0] := f[0](0) = 0, (D(f[0]))(0) = 0, (D(f[0]))(5) = 1;
for j to N do cond[1][j] := f[j](0) = 0, (D(f[j]))(0) = 0, (D(f[j]))(5) = 0 end do;
for i from 0 to N do dsolve({cond[1][i], equ[2][i]}, f[i](x)); assign(%) end do;

g := evalf@unapply(simplify(sum(f[n](x), n = 0 .. N)),x);
convert(g(x), 'rational');  
subs(x = 2.4, diff(g(x), x));


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convert(A,set):
indets(%,name);
fsolve(%%, % , (x->(x=0..1))~(%));

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Try one of these :

Button("Deduct", Evaluate(f = '[work(3), work(2)]'));
Button("Deduct", Evaluate(f = 'proc() work(3);  work(2) end()'));

How about this:

2.55*10^(-90);
op(%);
%[1]/10^Digits;
evalf(%,3);

Do You mean :

N := 4;
f:=unapply(sum(p^i*x, i = 0 .. N), x);
HPMEq := (1-p)*(diff(f(x), x$3))+p*(diff(f(x), x$3)+(1/2)*(diff(f(x), x, x))*f(x));

Edit:

i := 'i':
N := 4;
F := sum(p^i*f[i](x), i = 0 .. N);
HPMEq := (1 - p)*(diff(F, `$`(x, 3))) + p*((diff(F, `$`(x, 3))) + 1/2*(diff(F, x, x))*F);
for i from 0 to N do equ[2][i] := coeff(HPMEq, p, i) = 0 end do;

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Read title.
                           

Shouldn't this be like:

MySolution:=proc(xl :: algebraic, is :: {float, integer}, x :: algebraic)
if type(is, integer) then
   return solve(xl=is,x);
elif type(is, float) then
   return solve(xl=is,x);
end if;
end proc; 

See:

?gfun,algeqtodiffeq
with(gfun);
algeqtodiffeq(y = y^4+y^2*z+1, y(z));

also look at:
?algcurves,algfun_series_sol

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(diff(y(t), t))*(diff(y(t), t, t, t))-(diff(y(t), t))*y(t)^2-(diff(y(t), t))*(diff(y(t), t, t))-(diff(y(t), t))*A*y(t);
map(int, %, t);
student[intparts](%, diff(y(t), t));
(diff(y(t), t))*(diff(y(t), t, t))-(1/3)*y(t)^3-(1/2)*A*y(t)^2-(1/2)*(diff(y(t), t))^2+C+int((diff(y(s), s, s))^2, s = 0 .. t);
%-%%;

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