Consider the differential equation (1-x)y-xy' + py = 0, where p is a constant. (5a) Find...

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Consider the differential equation (1-x²)y"-xy' + p²y = 0, where p is a constant. (5a) Find two linearly independent series solutions valid for x < 1 (5b) Show that if p = n where n is a non-negative integer, then there is a polynomial solution of degree n. (5c) Determine the polynomial solutions from (5b) for n = 0, 1, 2, 3, 4. Consider the differential equation (1-x²)y"-xy' + p²y = 0, where p is a constant. (5a) Find two linearly independent series solutions valid for x < 1 (5b) Show that if p = n where n is a non-negative integer, then there is a polynomial solution of degree n. (5c) Determine the polynomial solutions from (5b) for n = 0, 1, 2, 3, 4.

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