Subtopic: Partial Differential Equations – Laplace, heat and wave equations
Question Statement:
The partial differential equation $\frac{\partial^2 u}{\partial x^2} - 7\frac{\partial^2 u}{\partial x \partial y} + 2\frac{\partial^2 u}{\partial y^2} = 0$ is said to be:
Options:
(A) parabolic
(B) hyperbolic
(C) elliptic
(D) eccentric
Official Answer Key:
B
Step-by-Step Solution & Explanation
For A·u_xx + B·u_xy + C·u_yy = 0, the discriminant B² − 4AC classifies the PDE: >0 hyperbolic, =0 parabolic, <0 elliptic. Here A=1, B=−7, C=2, so B²−4AC = 49−8 = 41 > 0 ⇒ hyperbolic. 'Eccentric' (D) is not a PDE classification and is a distractor.
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