math (differential equation)
posted by shoosh on .
show that y sub n=cos(ncos^1(x)) satisfies the differential equation:
(1x^2)(d^2y/dx^2)x(dy/dx)+n^2(dy/dx)=0

seems pretty straightforward:
y = cos(n arccos(x))
y' = n sin(n arccos(x)) / √(1x^2)
y'' = nx sin(n arccos(x))/(1x^2)^(3/2)  n^2 cos(n arccos(x))/(1x^2)
(1x^2) y'' = nx sin(n arccos(x))/√(1x^2)  n^2 cos(n arccos(x))
(1x^2) y''  xy' = n^2 cos(n arccos(x))
(1x^2) y''  xy'  n^2 y' doesn't make it go to zero.
That last step doesn't seem right. Is there a typo? Just the way it's shown doesn't seem right; two separate terms with y'