GATE Papers >> EEE >> 2019 >> Question No 13

Question No. 13 EEE | GATE 2019

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;\;\mathrm{where}\;c\neq0 $

is known as


Answer : (B) wave equation


Solution of Question No 13 of GATE 2019 EEE Paper

Given partial D.E

$ \frac{\partial^2\mathrm u}{\partial\mathrm t^2}-\mathrm C^2\left(\frac{\partial^2\mathrm u}{\partial\mathrm x^2}+\frac{\displaystyle\partial^2\mathrm u}{\displaystyle\partial\mathrm y^2}\right)=0,\;\mathrm{where}\;\mathrm C\neq0 $

$ \Rightarrow\frac{\partial^2\mathrm u}{\partial\mathrm t^2}=\mathrm C^2\left(\frac{\partial^2\mathrm u}{\partial\mathrm x^2}+\frac{\displaystyle\partial^2\mathrm u}{\displaystyle\partial\mathrm y^2}\right); $ which is clearly two dimensional wave equation.

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