Power series solution in Differential Equations

also I’m pretty Sure there are no mistakes for everything up until the 4th power term[I backed up my answer by Solving for y” and then differentiating 1 and 2 times respectively]

@Aneesh Srinivas Thanks for all. : )

I cannot see the steps clearly. I'm sure it's not caused from you. Is there any way to see clearly? or Could you share it with high resolution, if there is this type of option. If not THANKS FOR ALL again... I'm appreciate.

@Aneesh Srinivas If sharing solution via mail makes high the resolution, I add below my mail.

omerartuk7@gmail.com

Thanks