Consider the differential equation x³y(³) - 6xy' +12y = 0. (a) Find distinct values of r, say r₁, 72, ... rn so that y = x" is a solution of the differential equation for each i = 1, ... n. (b) Show that the set {x} is linearly independent. (c) What is the general solution of the differential equation? Reason out why it is the general solution. Refer to Chapter 3.

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A: Topic:- calculus and integration

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