I'm preparing for my exam and I have no idea how to do this kind of question.
part a) Let y= (1-x^2)^1/2 .arccosx. Show that (1-x^2)y' +xy +1-x^2 = 0
part b) Apply the Leibnitz rule to differentiate the equation in part a) n times with respect to x to obtain y(n+1) in terms of y(n-1)
part c) Use the result in Part b to evaluate the Maclaurin series of y up to x^4 .
I can do Part a) only but dunno how to do part b and c...