GATE CE 2024 Set 1 — Question 28
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Engineering Mathematics → Partial Differential Equations
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Question
For the following partial differential equation,which of the following option(s) is/are CORRECT?
Correct answer
(A) elliptic for x 0 and y 0; (D) hyperbolic for x < 0 and y 0
Solution
The general form of a second-order linear PDE is . The classification depends on the discriminant .
Given equation:
Here, , , and .
Discriminant .
Given equation:
Here, , , and .
Discriminant .
1.Elliptic: . This occurs when or . Thus, option (A) is correct.
2.Parabolic: or . Option (C) states elliptic for , which is incorrect as it is parabolic.
3.Hyperbolic: . This occurs when or . Thus, option (D) is correct.
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