GATE XE (Engineering Sciences) 2023 - Question 21

Section: Engineering Mathematics | Type: NAT | Marks: 2

Let 𝑢(𝑥, 𝑡) be the solution of the initial boundary value problem 𝜕𝑢 𝜕𝑡− 𝜕2𝑢 𝜕𝑥2 = 0, 𝑥∈(0, 2), 𝑡> 0 𝑢(𝑥, 0) = sin(𝜋𝑥), 𝑥∈(0, 2) 𝑢(0, 𝑡) = 𝑢(2, 𝑡) = 0. Then the value of 𝑒𝜋2 (𝑢( 1 2 , 1) −𝑢( 3 2 , 1)) is __________ (in integer).

Answer: 2