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GATE 2019 EE – Question 13

Engineering Mathematics · Differential Equations: First order equations, Higher order linear differential equations, Variation of parameters, Cauchy and Euler equations, Partial differential equations, Separation of variables · 1 mark · Multiple choice

The partial differential equation

$$\frac{\partial^2u}{\partial t^2}-c^2\left(\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}\right)=0;\quad\text{where }c\ne0$$

is known as

  1. heat equation
  2. wave equation
  3. Poisson's equation
  4. Laplace equation

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Show answer and explanation

Correct answer: (B) wave equation

Explanation

A second time derivative equal to $c^2$ times the spatial Laplacian is the wave equation.