Question

cosx=ycos(a+x) second order derivative

Answer 1

first order
-sinx=y(-sin(a+x))+dy/dxcos(a+x)
second order
-cosx=-(ycosx(a+x)+dy/dxsin(a+x))+(dy/dx(-sin(a+x))+d2y/dxcos(a+x))..
hope it is helpfull

Answer 2

Cos x = y Cos (a + x)

Differentiating wrt x :

- sin x = y' * Cos (a+x)  +  y ( -sin(a+x) ) * (a+x)'
y' * Cos(a+x) = y * Sin(a+x) - sin x

differentiating again wrt x

y'' * Cos(a+x) + y' *(-sin(a+x)) = y' * SIn(a+x) + y * COs(a+x) - cos x

y'' = 2 y' tan(a+x) + y - cosx / Cos(a+x)