The solution of the partial differential equation \frac{\partialu}{\partialt} = \alpha {\partial^{2}u}/{\partialx^{2}} is of the form

Correct Answer is : Cekt[C1e(kα)x+C2e−(kα)x]

C\cos ⁡ (kt) C_{1}e^{ (\sqrt{\frac{k}{\alpha }}) x} + C_{2}e^{− (\sqrt{\frac{k}{\alpha }}) x}

Ce^{kt}[C_{1}e^{ (\sqrt{\frac{k}{\alpha }}) x} + C_{2}e^{− (\sqrt{\frac{k}{\alpha }}) x}]

Ce^{kt}C_{1}\cos ⁡ (\sqrt{\frac{k}{\alpha }}) x + C_{2} \sin ⁡ (−\sqrt{\frac{k}{\alpha }}) x

C \sin ⁡ (kt) C_{1}\cos ⁡ (\sqrt{\frac{k}{\alpha }}) x + C_{2} \sin ⁡ (−\sqrt{\frac{k}{\alpha }}) x

GATE Civil Engineering (CE) 2016 Shift 1 Solved Paper

Question : 15 of 65

Marks: +1, -0

The solution of the partial differential equation

\;{∂u}/{∂t} = α \;{∂^{2}u}/{∂x^{2}}

is of the form

$C\cos ⁡ (kt) C_{1}e^{ (√{\;{k}/{α\;}}) x} + C_{2}e^{− (√{\;{k}/{α\;}}) x}$
$Ce^{kt}[C_{1}e^{ (√{\;{k}/{α\;}}) x} + C_{2}e^{− (√{\;{k}/{α\;}}) x}]$
$Ce^{kt}C_{1}\cos ⁡ (√{\;{k}/{α\;}}) x + C_{2} sin \;⁡ (−√{\;{k}/{α\;}}) x$
$C sin \;⁡ (kt) C_{1}\cos ⁡ (√{\;{k}/{α\;}}) x + C_{2} sin \;⁡ (−√{\;{k}/{α\;}}) x$

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