restart;
with(LinearAlgebra):
m:=4;

A:=Matrix([[0,0],[1/3,1/3]]);

b:=Vector([1/4,3/4]);

c:=Vector([0,2/3]);

n:=Dimension(b);

onesvector:=Vector(n,1);
fxi:=Vector([seq(f(t+c[i]*h,xi[i]),i=1..n)]);
xirhs:=y(t)*onesvector+h*Multiply(A,fxi);



T:=y(t+h)-y(t)-h*Multiply(Transpose(b),fxi);
for j from 1 to m-1
do
    T:=subs(xi=xirhs,T);
od:

S:=series(T,h,m);

eq[1]:=D(t->y(t))(t)=f(t,y(t));

for j from 1 to m-2
do
    eq[j+1]:=simplify(subs(seq(eq[i],i=1..j),D(unapply(eq[j],t))(t)));
od;


simplify(subs(seq(eq[i],i=1..m-1),S));