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

Correct Answer is : u=U(1−ekx1−ekL)

u = U ( {1−e^{kx}}/{1−e^{kL}})

u = U ( {1−e^{−kx}}/{1−e^{−kL}})

u = U ( {1 + e^{−kx}}/{1 + e^{−kL}})

GATE Mechanical Engineering (ME) 2013 Solved Paper

Question : 56 of 65

Marks: +1, -0

The solution to the differential equation

\;{d^{2}u}/{dx^{2}}−k\;{du}/{dx} = 0

where k is a constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is

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