# GATE ME 2013 | Question: 46

The solution to the differential equation $\dfrac{d^2u}{dx^2}-k\dfrac{du}{dx}=0$  where $k$ is a constant, subjected to the
boundary conditions $u(0)$ = $0$ and $u(L)$ = $U$, is

1. $u=U\dfrac{x}{L}$
2. $u=U\left(\dfrac{1-e^{kx}}{1-e^{kL}}\right)$
3. $u=U\left(\dfrac{1-e^{-kx}}{1-e^{-kL}}\right)$
4. $u=U\left(\dfrac{1+e^{kx}}{1+e^{kL}}\right)$

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