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GATE 2025 AE – Question 14

Engineering Mathematics · Differential Equations: Classification of PDEs, wave, Laplace and heat equations by separation of variables · 1 mark · Multiple choice

The partial differential equation $\frac{\partial^2 u}{\partial x^2} + 4\frac{\partial^2 u}{\partial x \partial y} + 2\frac{\partial^2 u}{\partial y^2} = 0$ is ______.

  1. elliptic
  2. hyperbolic
  3. parabolic
  4. of mixed type

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Correct answer: (B) hyperbolic

Explanation

For $Au_{xx} + Bu_{xy} + Cu_{yy} = 0$ the type is decided by $B^2 - 4AC$. Here $A = 1$, $B = 4$, $C = 2$, so $B^2 - 4AC = 16 - 8 = 8 > 0$, which is hyperbolic.