GATE CE 2017 Set 2 — Question 29
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Engineering Mathematics → Ordinary Differential Equations → Complementary Function & PI
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Question
Consider the following second-order differential equation:The particular solution of the differential equation is
Correct answer
(A) -2 - 2t - t²
Solution
The given differential equation is .
Since the right-hand side is a polynomial of degree 2, we assume a particular solution of the form:
Then,
Substituting these into the differential equation:
Comparing coefficients of like powers of :
1)
2)
3)
So, the particular solution is:
This matches option (A).
Since the right-hand side is a polynomial of degree 2, we assume a particular solution of the form:
Then,
Substituting these into the differential equation:
Comparing coefficients of like powers of :
1)
2)
3)
So, the particular solution is:
This matches option (A).
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