Teaching JKPSC Lecturership Mock Test Series 2024-25 Mathematical Science Partial Differential Equations Laplace Equation, Heat and Wave Equations
Let u(x, t) be the solution of
utt − uxx = 0, 0 < x < 2, t > 0
u(0, t) = 0 = u(2, t), ∀ t > 0,
u(x, 0) = sin (πx) + 2 sin(2πx), 0 ≤ x ≤ 2,
ut(x, 0) = 0, 0 ≤ x ≤ 2.
Which of the following is true?
1
u(1, 1) = −1.
2
u(1/2, 1) = 0.
3
u(1/2, 2) = 1.
4
ut(1/2, 1/2) = π.