Allied & ICAR Exam Bank • ALLIED_2722 NAT • 2 Marks

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 a parabolic PDE. The discriminant $B^2 - 4AC$ is:

Answer Key:

0

Step-by-Step Solution & Explanation

For second-order PDE $A u_{xx} + B u_{xt} + C u_{tt} + \dots = 0$, here $A = \alpha, B = 0, C = 0$. Discriminant $B^2 - 4AC = 0 - 0 = 0$. A zero discriminant defines parabolic PDEs.
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