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A function $n(x)$ satisfies the differential equation $\frac{d^{2} n(x)}{d x^{2}}-\frac{n(x)}{L^{2}}=0$ where $L$ is a constant. The boundary conditions are: $\pi(0)=K$ and $n(\infty)=0$. The solution to this equation is

- $n(x)=K \exp (x / L)$
- $n(x)=K \exp (-x / \sqrt{L})$
- $n(x)=K^{2} \exp (-x / L)$
- $n(x)=K \exp (-x / L)$