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Q#1 Differential Equations GATE CH 2022 MCQ +2 marks -0.66 marks

The partial differential equation

                                             .

where, 𝑡 ≥ 0 and 𝑥  [0,1], is subjected to the following initial and boundary conditions:

                                                𝑢(𝑥, 0) = sin ( 𝜋𝑥)          

                                                     𝑢(0, 𝑡) = 0

                                                     𝑢(1, 𝑡) = 0

The value of 𝑡 at which .

1

e

𝜋

1/e

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