2. (50) Show that the differential equation 3x°y" +2xy' + a*y = has a regular singular point at x 0. Determine the indicial equation, the recurrence relation, and the roots of the indicial equation. Find the series solution (x > 0) corresponding to the larger root: If the roots are unequal and do not differ by an integer, find the series solution corresponding to the smaller root also.

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