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GATE 2016 CE (CE1) – Question 12

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

The partial differential equation $P_{xx}+P_{yy}+3P_{xy}+2P_x-P_y=0$ is ______.

  1. Elliptic
  2. Parabolic
  3. Hyperbolic
  4. None of these

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Show answer and explanation

Correct answer: (C) Hyperbolic

Explanation

Use the principal part A Pxx+2B Pxy+C Pyy. Here A=C=1 and2B=3, giving B²−AC=2.25−1=1.25>0. The equation is therefore **hyperbolic, C**. First-order terms do not affect this classification.