GATE EC 2022 Set 1 — Question 25
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Engineering Mathematics → Differential Equations → PDE by Separation of Variables
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Question
Consider the following partial differential equation (PDE)where and are distinct positive real numbers. Select the combination(s) of values of the real parameters and such that is a solution of the given PDE.
Correct answer
(A) = 1√(2a), = 1√(2b); (B) = 1√(a), = 0
Solution
Given the PDE:
Substitute into the equation:
Plugging these into the PDE:
Dividing by (which is never zero):
Now, check the options:
(A) . (Correct)
(B) . (Correct)
(C) . (Incorrect)
(D) . (Incorrect)
Substitute into the equation:
Plugging these into the PDE:
Dividing by (which is never zero):
Now, check the options:
(A) . (Correct)
(B) . (Correct)
(C) . (Incorrect)
(D) . (Incorrect)
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