1. The Legendre equation of order p is, (1 - 2%)/" - 2xy + p(p+1)y = 0. a) Find the associated Euler equation and the characteristic equation for x = 1. b) Find the first three nonzero terms in one of the power series solution in powers of 2 - 1 for 2-1 > 0. (Hint: Write 1+r = 2 + (1 - 1) and r = 1 + (1 - 1). Alternatively, make the change of variable r - 1 = t and determine the series solution in powers of t. 1. The Legendre equation of order p is, (1 - 2%)/" - 2xy + p(p+1)y = 0. a) Find the associated Euler equation and the characteristic equation for x = 1. b) Find the first three nonzero terms in one of the power series solution in powers of 2 - 1 for 2-1 > 0. (Hint: Write 1+r = 2 + (1 - 1) and r = 1 + (1 - 1). Alternatively, make the change of variable r - 1 = t and determine the series solution in powers of t