By letting

we get derivatives


a) Substitute these into the differential equation. After a lot of simplification, the equation reduces to

Examine the lowest degree term
, which gives rise to the indicial equation,

with roots at r = 0 and r = 4/5.
b) The recurrence for the coefficients
is

so that with r = 4/5, the coefficients are governed by

c) Starting with
, we find


so that the first three terms of the solution are

Three equivalent fractions:
2/3
4/6
16/24
Remember PEMDAS
Do parentheses, results in 25. So whats left is 87-25*(-3)+9
Then you multiply -25 by -3, answer is 75. 87+75+9
Add all of them up. 171
The answer is 171!
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