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Integrating factor of a linear differential equation

This type of question, asked 5 times: 9 May 2023 S2, 18 Apr 2026 S2, 20 Apr 2026 S1, 12 May 2026 S2, 19 May 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    9 May 2023 S2

    149
    Integrating factor of the differential equation dydx+y=1+yx\frac{dy}{dx} + y = 1 + \frac{y}{x} is

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  2. Question 2

    18 Apr 2026 S2

    85
    The integrating factor of the differential equation xdydx+2y=x2log⁡xx\dfrac{dy}{dx} + 2y = x^2\log x is

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  3. Question 3

    20 Apr 2026 S1

    86
    If tan⁡x\tan x is an integrating factor of the differential equation dydx+Py=Q\dfrac{dy}{dx} + Py = Q, then PP can be

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  4. Question 4

    12 May 2026 S2

    86
    If g(x)g(x) denotes the integrating factor of the differential equation xlog⁡xdydx+y=2log⁡xx\log x\dfrac{dy}{dx} + y = 2\log x and ∫g(x) dx=h(x)[g(x)−1]+c\displaystyle\int g(x)\,dx = h(x)[g(x) - 1] + c, then h(x)=h(x) =........

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  5. Question 5

    19 May 2026 S2

    88
    Which of the following is not a correct pair of a linear differential equation and its integrating factor?

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