Verifying perturbation theory proof mentioned in an online article

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I am reading an article mentioned here http://www.bcamath.org/documentos_public/archivos/personal/comites/course.pdf. I am stuck at page 14 where it says "Thus from (2.1.7) it follows that the coefficient of $\epsilon^{\alpha0}$ should be zero, namely $x_0 = 0$". I couldn't prove how coeffecient $x^0$ becomes zero.