Mathematics

Problem

The differential equation

\frac{d^2y}{dx^2} = -\sin y

, with

y = \frac{\pi}{2}

\frac{dy}{dx} = 0

x = 0

. a. a Find the values of

\frac{d^2y}{dx^2}

\frac{d^3y}{dx^3}

and

\frac{d^4y}{dx^4}

x = 0

. b. b Hence find the Maclaurin series for

y

, up to and including the term in

x^4