Show that x 0 is a regular singular pointfind two linearly, Mathematics

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Show that x 0 is a regular singular pointfind two linearly

1. For y''-xy'-y=0 about x₀=1 find the first four non-zero terms of two linearly independent solutions y₁ (x) and y₂ (x) .

2. For x²y" xy' +[x²-(1/9)]y=0

a. Show that x = 0 is a regular singular point.

b. Find two linearly independent solutions about this point using the Frobenius Method.

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Mathematics: Show that x 0 is a regular singular pointfind two linearly

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Mathematics: Show that x 0 is a regular singular pointfind two linearly

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