Consider the following differential equation: r*(1– 2x)y" + 3xy' +(1+4x)y = 0 (2) a) Find the singular and ordinary points of Equation (2). Next, show that x, = 0 is a regular singular point of Equation (2). (b) Determine the series solutions of Equation (2) at the regular singular point x, = 0 using suitable method. Show details of your work indicating the indicial equation, roots of indicial equation, and the recurrence relation, where relevant.

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