GATE EC 2020 Set 1 — Question 14
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Engineering Mathematics → Differential Equations → Higher-Order Linear ODEs
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Question
The general solution of is
Correct answer
(C) y = (C₁+C₂x)e^(3x)
Solution
The given differential equation is a second-order linear homogeneous differential equation with constant coefficients:The characteristic equation is found by replacing with , with , and with :This is a perfect square trinomial:So, we have repeated roots: .
For repeated real roots , the general solution is of the form:Substituting :Comparing this with the given options, option (C) matches.Therefore, the correct answer is (C).
For repeated real roots , the general solution is of the form:Substituting :Comparing this with the given options, option (C) matches.Therefore, the correct answer is (C).
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