If $y = x^{3}$ and $x^{2}\frac{d^2y}{dx^2} = ky$, what is $k$?

Explanation

1. 01

   $\frac{dy}{dx} = 3x^{2}$ and $\frac{d^2y}{dx^2} = 6x$.

2. 02

   $x^{2} \cdot 6x = 6x^{3} = 6y$, so $k = 6$.