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
Answer:
Step-by-step explanation:
F [First terms] - Multiply the first terms in each set of parentheses FARTHEST TO THE LEFT
O [Outside terms] - Multiply the first term in the first set of parentheses FARTHEST TO THE LEFT by the last term in the second set of parentheses FARTHEST TO THE RIGHT
I [Inside terms] - Multiply the last term in the first set of parentheses FARTHEST TO THE RIGHT by the first term in the second set of parentheses FARTHEST TO THE LEFT
L [Last terms] - Multiply the last terms in each set of parentheses FARTHEST TO THE RIGHT
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