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GATE 2026 AE – Question 13

Engineering Mathematics · Differential Equations: Classification of PDEs, wave, Laplace and heat equations by separation of variables · 1 mark · Multiple choice

The following equation with respect to $\varphi(x, t)$, where $a$ is a non-zero constant, represents ________.

$\frac{\partial \varphi}{\partial t} + a \frac{\partial \varphi}{\partial x} = 0$

  1. linear wave propagation
  2. transient heat conduction
  3. Newton's law of cooling
  4. radiative transfer

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Show answer and explanation

Correct answer: (A) linear wave propagation

Explanation

This first-order equation has the solution $\varphi = f(x - at)$: a profile that moves with speed $a$ without changing shape. It is the linear wave (advection) equation. Heat conduction would have a second derivative in $x$.