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GATE ECE 2010 | Question-3

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

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