Allied & ICAR Exam Bank • ALLIED_0076 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

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

Question Statement:

The one-dimensional heat conduction equation $\frac{\partial u}{\partial t} = \alpha \frac{\partial^2 u}{\partial x^2}$ is classified as:

Options:

  • (A) Parabolic PDE
  • (B) Hyperbolic PDE
  • (C) Elliptic PDE
  • (D) Non-linear ODE

Answer Key:

A

Step-by-Step Solution & Explanation

The diffusion/heat equation is parabolic ($B^2 - 4AC = 0$). Wave equation is hyperbolic, Laplace equation is elliptic.
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