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GATE 2018 ME (ME2) – Question 13

Engineering Mathematics · Differential Equations: Heat, wave and Laplace equations · 1 mark · Multiple choice

For a function $u(x,t)$, $\frac{\partial u}{\partial t}=\frac{\partial^2u}{\partial x^2}$ is the ______.

  1. wave equation
  2. heat equation
  3. Laplace equation
  4. elasticity equation

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Show answer and explanation

Correct answer: (B) heat equation

Explanation

A first time derivative equated to a positive spatial second derivative describes diffusion, specifically the one-dimensional **heat equation, B**, with unit diffusivity. The wave equation instead contains a second time derivative.