find-y-n-if-y-cos-2x-

Question Number 8488 by Basant007 last updated on 12/Oct/16

f i n d y_{n} i f y = \cos 2 x

Commented by FilupSmith last updated on 13/Oct/16

y_{n} = \frac{d^{n} y}{{d x}^{n}}

y_{1} = \frac{1}{2} \sin (2 x)

y_{2} = - \frac{1}{4} \cos (2 x)

y_{3} = \frac{1}{8} \sin (2 x)

y_{4} = - \frac{1}{16} \cos (2 x)

∴ y_{n} = {(- 1)}^{n + 1} \frac{1}{2^{n}} \times ? ? ?

working / / / thinking

Commented by Rasheed Soomro last updated on 13/Oct/16

What relation is there between

y_{n} and y = \cos 2 x ?

Commented by Basant007 last updated on 13/Oct/16

f i n d u s i n g s u c c e s i v e d i f f e r e n t i a t i o n

Commented by Basant007 last updated on 13/Oct/16

i . e y_{n}

Commented by FilupSmith last updated on 13/Oct/16

y_{n} = {\begin{cases} \frac{1}{2^{n}} \sin (2 x) if 2 ∣ n \\ - \frac{1}{2^{n}} \cos (2 x) if 2 ∤ n \end{cases}

Commented by Basant007 last updated on 13/Oct/16

i tried and got this

Commented by Basant007 last updated on 13/Oct/16

y_{n} = a^{n} \cos {n \frac{π}{2} + 2 x}