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Please help me solve this ode with power series.

I am struggling to solve this ode about z=0(singular point)

$$\zy"-2y'+9(z^5)y=0$$
I have followed the regular frobeneus method and found \sigma=0,3

Assumed solution is $$ \sum_{i=0}^~ a_{n} y^{n+\sigma} $$
when I put \sigma = 0 I get

(n+3)(n)a_n+9a_(n-6)=0
From this I can find out

a_{6}=-{9/n(n+3)}a_{6p-6}

From there I cant find out how to proceed to get recursion relation between and find the actual solution.

I can understand that I should get 2 equations but I cant find out none of the closed form or series accurately.
Thank you in advance for your kind help.

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