Let u(x, y) be the solution of ∂2u∂x2 + ∂2u∂y2 = 64 in the unit disc {(x, y) | x2 + y2 < 1} such that u vanishes on the boundary of the disc. Then the value of u(1/4, 1/√2) is equal to:

Let u(x, t) be the solution of the initial value problem: utt - uxx = e-t, x ∈ ℝ, t > 0, u(x, 0) = cos x, ut(x, 0) = 0, x ∈ ℝ. Then which of the following statements is true?

Consider the initial-boundary value problem (IBVP): ut + ux = 0, 0 0, u(x, 0) = ex, 0 0. Which of the following statements is true?