GATE EC 2017 Set 1 — Question 29
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Engineering Mathematics → Differential Equations → First-Order Nonlinear Equations
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Question
Which one of the following is the general solution of the first order differential equation , where are real?
Correct answer
(D) y = 1 - x + tan(x + c), where c is a constant.
Solution
Given the differential equation:Let . Differentiating both sides with respect to :Substituting from the original equation:This is a separable differential equation:Integrating both sides:Substituting back :This matches option (D).
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