Question: The point x = 0 is a regular singular point of the given differential equation. 4xy - y' + 4y = 0 Show that the

The point x = 0 is a regular singular point of
The point x = 0 is a regular singular point of the given differential equation. 4xy" - y' + 4y = 0 Show that the indicial roots / of the singularity do not differ by an integer. (List the indicial roots below as a comma-separated list.) r Use the method of Frobenius to obtain two linearly independent series solutions about x = 0. Form the general solution on (0, co). oy = C1X5/4(1 - 4x + 8x 323 + 8x2 + + C2 1 4x 32x3 7 + 5 135 77 3465 oy = C1 1 -x+x + + C2x5/4( 1 - x + 2 + 4 36 4 36 oy = C1x5/4( 1 + 4x - 8x2 + 32x3 + ... + C2 1 - 4x + 8x2 323 + 3 63 9 117 5967 oy = C1 1 + 4x - 8x + 32x3 + + 3 + ...) + C2x5/4 ( 1 - . 4x 8x2 32x3 63 9 117 5967 o y = C1 1 - 4x + 8x2 32x3 + ..+ C2x5/4/ 1 4x + 8x2 32x3 + 5 135 77 3465

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