Question Bank • QB_EM_ADV_065 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Partial Differential Equations – Laplace, heat and wave equations

Question Statement:

The two-dimensional wave equation $\frac{\partial^2 u}{\partial t^2} = c^2 \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \right)$ is mathematically classified as:

Options:

  • (A) Hyperbolic
  • (B) Parabolic
  • (C) Elliptic
  • (D) Ultra-hyperbolic

Answer Key:

A

Step-by-Step Solution & Explanation

In standard second-order partial differential equation classification: - Wave equation (second-order in time and space with opposite signs): Hyperbolic - Heat/diffusion equation (first-order in time, second-order in space): Parabolic - Laplace/Poisson equation (elliptic operator without time): Elliptic
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