Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Partial Differential Equations Laplace Equation, Heat and Wave Equations
Let u(x, t) be a smooth solution to the wave equation
(∗) \(\frac{\partial^2 u}{\partial t^2}-\frac{\partial^2 u}{\partial x^2}=0\) for (x, t) ∈ ℝ2.
Which of the following is FALSE?
1
u(x - θ, t) also solves the wave equation (∗) for any fixed θ ∈ ℝ.
2
\(\frac{\partial u}{\partial x}\) also solves the wave equation (∗).
3
u(3x, 9t) also solves the wave equation (∗).
4
u(3x, 3t) also solves the wave equation (∗).
5
Question Not Attempted