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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)

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

From this I can find out


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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