hey guys,
I've been trying to solve this question,
so the general solution would be
y(cos(theta)) = C Pn(cos(theta)) + D Qn(cos(theta)) right?
and since n = 2 in this case
y(cos(theta)) = C P_2 (cos(theta)) + D Q_2 (cos(theta))
and 0<= theta < 2Pi
But when theta = 0, cos(theta) = 1 and Q_2 is undefined, so D = 0,
so y(cos(theta)) = C P_2 (cos(theta)) = (C/2) (cos^2(theta) - 1)
but
y(cos(0))=y(1) = C P_2(1) = C = ?
So would the 2pi periodic solution be
y(cos(theta)) = (C/2) (cos^2(theta) - 1) ?
Thanks