restart;
read "eg.mpl":
sys := Matrix([[-1-x+x^2-Sum(x^k,k=3..infinity),-x^2,-1-x],
[-x^2,-Sum(x^k,k=1..infinity),-1-x^3],
[-x^3,x,-Sum(x^k,k=0..infinity)]]).y(x)+
Matrix([[x^2,0,0],[0,1,0],[0,0,1]]).theta(y(x),x,1)+
Matrix([[x+Sum(x^k,k=3..infinity),0,0],
[0,Sum(x^k,k=1..infinity),0],
[0,0,Sum(x^k,k=1..infinity)]]).theta(y(x),x,2);
JSFH
EG:-LaurentSolution(sys, theta, y(x), 0);
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Res := EG:-FormalSolution(sys, theta, y(x), t, 'solution_dimension' = 6):
Res[1]; Res[2]; Res[3];
JSFH
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