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GATE 2020 CE (CE1) – Question 11

Engineering Mathematics · PDE: Fourier series, separation of variables, diffusion, wave and Laplace equations · 1 mark · Multiple choice

In $$D(\theta)\frac{\partial^2\theta}{\partial z^2}+\frac{\partial K(\theta)}{\partial z}-\frac{\partial\theta}{\partial t}=0,$$ θ is a function of t and z, and D and K are functions of θ. Classify the equation.

  1. Second-order linear
  2. Second-degree linear
  3. Second-order nonlinear
  4. Second-degree nonlinear

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Show answer and explanation

Correct answer: (C) Second-order nonlinear

Explanation

The highest derivative is second order in z. Its coefficient D depends on the unknown θ,and differentiating K(θ) introduces K′(θ)θz. In general these dependencies make the equation nonlinear. It is **second-order nonlinear,C**,not second-degree merely because a second derivative occurs.