Question

\(y=x^2(cosx)\) is a solution to \(x^2y^{(2)} - 4xy^{(1)} + (x^2+6)y =0 \), where \(y^{(n)} =\frac{d^ny}{dx^n}\).
Show, when x=0, \((n-2)(n-3)y^{(n)} = -n(n-1)y^{(n-2)}\).

Answer 1

Oh! Just a minute, let me try to do it first!

Answer 2

Sorry that it actually takes me an hour to do it!!
I would like to ask if I can say \(-(cosx)^{(n-4)} = (cosx)^{(n-2)}\)?