The equation (1- t 2)y"- 2ty' + a(a + l)y = 0, a constant, is known as the legendre differential equation, and it appears in many areas of mathematics and physics. (a) find 2 linearly independent solutions of the legendre equation. (b) show that the legendre differential equation has a polynomial solution of degree n if a = n. (c) the legendre polynomial pn(t) is defined as the polynomial solution of the legendre equation with a = n which satisfies the condition pn(l) = 1. find p0(t), p1(t), pz(t), and p3(t).