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Bernoulli equation: divide by a power of y and substitute

This type of question, asked 5 times: 16 May 2023 S2, 11 May 2024 S2, 25 Apr 2025 S1, 11 Apr 2026 S2, 13 May 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    16 May 2023 S2

    142
    The general solution of the differential equation dydx=ytan⁡x−y2sec⁡x\frac{dy}{dx} = y\tan x - y^2\sec x is

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  2. Question 2

    11 May 2024 S2

    107
    The solution of dxdy+xy=x2\frac{dx}{dy} + xy = x^2 is:

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  3. Question 3

    25 Apr 2025 S1

    123
    The solution of the equation x2y−x3⋅ dy dx=y4cos⁡xx^{2}y-x^{3}\cdot\frac{\text{ }dy}{\text{ }dx}=y^{4}\cos x, where y(0)=1y(0) = 1, is

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  4. Question 4

    11 Apr 2026 S2

    86
    The solution of the differential equation xdydx+y=x3y6x\dfrac{dy}{dx} + y = x^3y^6, is...

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  5. Question 5

    13 May 2026 S2

    87
    If the curve y=f(x)y = f(x) passes through the point (1,2)(1, 2) and satisfies the differential equation xdy+(y+x3y2)dx=0xdy + (y + x^3y^2)dx = 0, then the equation of curve is...

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