Allied & ICAR Exam Bank • ALLIED_2721
MCQ • 1 Mark
Section 1: Engineering Mathematics
Differential Equations
Subtopic: Partial Differential Equations – Laplace, heat and wave equations
Question Statement:
In partial differential equation classification, the second-order wave equation $\frac{\partial^2 u}{\partial t^2} - c^2 \frac{\partial^2 u}{\partial x^2} = 0$ ($c > 0$) is classified as:
Options:
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(A) Hyperbolic
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(B) Parabolic
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(C) Elliptic
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(D) Non-linear
Step-by-Step Solution & Explanation
Discriminant $B^2 - 4AC$: here $A = c^2, B = 0, C = -1 \implies 0 - 4(c^2)(-1) = 4c^2 > 0$. Hence it is strictly hyperbolic.
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