GATE CE 2016 Set 1 — Question 40
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Engineering Mathematics → Ordinary Differential Equations → Complementary Function & PI
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Question
The respective expressions for complimentary function and particular integral part of the solution of the differential equation are
Correct answer
(A) [c₁ + c₂ x + c₃ sin √(3)x + c₄ cos √(3)x] and [3x⁴ - 12x² + c]
Solution
The given differential equation is .1. Complementary Function (CF):
The auxiliary equation is .
Roots are .
For repeated real roots , the part of CF is .
For complex roots , the part of CF is .
So, .2. Particular Integral (PI):
.Comparing with the options, Option (A) matches both CF and PI (the constant in PI is redundant but present in the option).
The auxiliary equation is .
Roots are .
For repeated real roots , the part of CF is .
For complex roots , the part of CF is .
So, .2. Particular Integral (PI):
.Comparing with the options, Option (A) matches both CF and PI (the constant in PI is redundant but present in the option).
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