GATE CE 2014 Set 2 — Question 14
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Engineering Mathematics → Ordinary Differential Equations → First-Order Linear Equations
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Question
The integrating factor for the differential equation is
Correct answer
(D) e^(k₂ t)
Solution
To find the integrating factor of the given differential equation, we first identify its form. The given first-order linear ordinary differential equation is:A standard first-order linear differential equation in terms of the dependent variable and independent variable is written as:By comparing the given equation with the standard form, we identify:The integrating factor () for such a differential equation is given by the formula:Substituting into the formula:Since is a constant:Therefore, the integrating factor is .Correct Option: D
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