Question: The point x = 0 is a regular singular point of the given differential equation. xy + 2y' - xy = 0 Show that

The point x = 0 is a regular singular point of
The point x = 0 is a regular singular point of the given differential equation. xy " + 2y' - xy = 0 Show that the indicial roots / of the singularity differ by an integer. (List the indicial roots below as a comma-separated list.) r= Use the method of Frobenius to obtain at least one series solution about x = 0. Use (23) in Section 6.3 e -SP ( x ) dx y2(x) = 1 1(x) / -dx (23) y 1 ( x ) where necessary and a CAS, if instructed, to find a second solution. Form the general solution on (0, co). oy = . X C1 sinh x + C2 cosh x X oy = - C1 sin x + C2 cos x oy = x Cj sin x + C2 cos x oy= x2 C1 sinh x + C2 oy = x C1 sinh x + C2 cosh x

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