cdf =Manipulate[Column[{ SuFunc[ff, aa, yy0, nn]}],Style[escriba@proposito,Bold,10],Spacer[{100,3}],
 (*Inicio contadores *)
 {{f,5t+3y,"f = "},ControlType->InputField},
{{a,2,"a = "},ControlType->InputField},
{{y0,1,"y(a) = "},ControlType->InputField},
(*{{b,3,"b = "},ControlType->InputField},*)
{{n,4,"Orden n="},ControlType->InputField},
Button["OK", ff=f; aa=a; yy0 =y0; nn=n]
(* Fin contadores *)
,Alignment->Center,Deployed->True,AppearanceElements->"ResetButton",LocalizeVariables->True,ContinuousAction->False,FrameLabel->{{None,None},{Column[{,Row[{Style["Autores: Juan Félix Ávila Herrera y Enrique Vílchez Quesada",Bold,10,RGBColor[0,0,0.5]]}],Row[{Style["Escuela de Informática | Universidad Nacional de Costa Rica",Bold,10,RGBColor[0.5,0.1,0]]}]},Center],Style["Título: Aproximaciones sucesivas de Picard.", Bold,14, RGBColor[0,0.33,0.33]]}},
Initialization:>(
ClearAll["Global`*"];
ff=f; aa=a; yy0 =y0; nn=n;
escriba[lista_]:=Style[Row@lista,Black];
(*($PreRead=(#/. s_String/;StringMatchQ[s,NumberString]&&Precision@ToExpression@s==MachinePrecision:>s<>"`12."&))*);
proposito ={"Propósito: Hallar mediante el método de Picard la n-ésima\naproximación  de la EDO y'=f(t, y)",  ", y(a)=", (Subscript[y, 0]),  ", con ", "a≤ t≤ b.\nNota. Se usa la regla simple de Simpson para aproximar las integrales"};
SuFunc[f_, a_, y0_, n_] := Module[{r},  
y[t_] =y0;
g[x_] := f/.{t-> x, y-> y[x]};
r ={(Subscript[y, 0]),"=", y0, "\n"};
Do[y[t_]=y0+ ((t-a)/6)(g[t]+g[a]+4g[((a+t)/2)]) ; 
 r = Join[r, { (Subscript[y, i]), "=",Expand@Simplify@y[t], "\n"}];, {i, 1, n}]; 
escriba@r

];

)]
(*CloudDeploy[cdf, Permissions->"Public"]*)