Suppose $y = c_{1}\cos\!\left(kx\right)+c_{2}\sin\!\left(kx\right)$ where $k > 0$ is a constant, and $c_1$ and $c_2$ are arbitrary constants. Find the following. Enter $c_1$ as c1 and $c_2$ as c2.

1. $\displaystyle \frac{dy}{dx} =$ help (formulas)
   
   
2. $\displaystyle \frac{d^2y}{dx^2} =$ help (formulas)
   
   
3. Rewrite your answer to the previous part in terms of $y$.
   $\displaystyle \frac{d^2y}{dx^2} =$ help (formulas)
   
   
4. Find the general solution to $\displaystyle \frac{d^2y}{dx^2} = - 16 y$. Enter your answer as an equation $y = \ldots$.
   
   help (equations)