The equation (1 - t^2)y" - 2ty' a(a 1)y = 0, is known as the Legendre differential equation.Find two linearly independent solutions of the Legendre equation.b) Show that the Legendre equation has a polynomial solution of degree n if a = n.The Legendre polynomial, Pn(t), is defined as the polynomial solution of the Legendre equation and satisfies the condition Pn(1) = 1.Find P0(t), P1(t), P2(t), and Pn(t).

Find the analytical solutions of the following time-varying lin... | Filo

Example 4 (i) - Find two solutions for equation: 4x 3y = 12