Allied & ICAR Exam Bank • ALLIED_2723 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Partial Differential Equations – Laplace, heat and wave equations

Question Statement:

The two-dimensional Laplace equation $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0$ is classified as:

Options:

  • (A) Elliptic
  • (B) Parabolic
  • (C) Hyperbolic
  • (D) Homoclinic

Answer Key:

A

Step-by-Step Solution & Explanation

Here $A = 1, B = 0, C = 1 \implies B^2 - 4AC = -4 < 0$. Negative discriminant defines elliptic PDEs.
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