Frobenius methon for ODE

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I was reading about Frobenius method for solving 2nd order ODE and I found two examples which I couldn´t solve. I would appreciate any kind of help:

  1. ${u}''-2u'+(1+\frac{1}{4z^2})u=0$
  2. ${u}''+\frac{1-z}{z(1+z)}u'-\frac{1-z}{z(1+z)^2}=0$