GATE (TF) Textile 2007 Question Paper Solution | GATE/2007/TF/26

Question 26 (Textile Engineering & Fibre Science)

By applying the method of separation of variables [u(x,t)=X(x)T(t)] to the heat equation

    \[\frac{\partial u}{\partial t}=c^2 \frac{\partial^2u}{\partial x^2}\]

and assuming -k^2 as the separation constant, its solution is obtained as

(A)u(x,t)=[c_1sin(kt)+c_2cos(kt)]exp(-k^2c^2x)
(B)u(x,t)=[c_1sinh(kt)+c_2cosh(kt)]exp(-k^2c^2x)
(C)u(x,t)=[c_1sin(kx)+c_2cos(kx)]exp(-k^2c^2t)
(D)u(x,t)=[c_1sinh(kx)+c_2cosh(kx)]exp(-k^2c^2t)
[Show Answer]

Option C is correct.

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