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Differential Equations

MHT-CET Maths. Try each one first, then open its answer.

Top 10 MHT-CET PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 15 times: May 2021 S1, 3 May 2023 S2, 4 May 2023 S2, 10 May 2023 S2, 15 May 2023 S2, 10 May 2024 S1, 11 May 2024 S1, 12 May 2024 S2, 14 May 2024 S1, 21 Apr 2025 S1, 21 Apr 2025 S2, 26 Apr 2025 S1, 15 Apr 2026 S1, 15 Apr 2026 S2, 19 May 2026 S1. This one: 19 May 2026 S1 See all 15 of this type

    89
    The solution of the differential equation dydx=xy+yxy+x\dfrac{dy}{dx} = \dfrac{xy + y}{xy + x} is

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  2. Question 2

    This type asked 14 times: May 2021 S1, 3 May 2023 S1, 3 May 2023 S2, 20 Apr 2025 S1, 22 Apr 2025 S1, 23 Apr 2025 S1, 11 Apr 2026 S1, 15 Apr 2026 S2, 16 Apr 2026 S2, 18 Apr 2026 S2, 20 Apr 2026 S1, 20 Apr 2026 S2, 14 May 2026 S1, 15 May 2026 S1. This one: 15 May 2026 S1 See all 14 of this type

    87
    The order and degree of the differential equation edydx+dydx=xe^{\frac{dy}{dx}} + \dfrac{dy}{dx} = x is

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  3. Question 3

    This type asked 11 times: 4 May 2023 S2, 15 May 2023 S1, 14 May 2024 S1, 20 Apr 2025 S1, 22 Apr 2025 S2, 25 Apr 2025 S1, 26 Apr 2025 S1, 11 Apr 2026 S1, 13 Apr 2026 S2, 13 May 2026 S2, 19 May 2026 S2. This one: 19 May 2026 S2 See all 11 of this type

    86
    If y=c1sin⁡2x+c2y = c_1\sin^2 x + c_2, then its differential equation is:

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  4. Question 4

    This type asked 11 times: 10 May 2023 S1, 10 May 2024 S2, 11 May 2024 S2, 20 Apr 2025 S1, 22 Apr 2025 S1, 26 Apr 2025 S2, 15 Apr 2026 S1, 18 Apr 2026 S1, 19 Apr 2026 S2, 20 Apr 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 11 of this type

    87
    The general solution of the differential equation (x+1)dydx−y=ex(x+1)2(x + 1)\dfrac{dy}{dx} - y = e^x(x + 1)^2 is given by:

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  5. Question 5

    This type asked 11 times: 9 May 2023 S1, 9 May 2023 S2, 11 May 2023 S1, 16 May 2023 S2, 10 May 2024 S2, 12 May 2024 S1, 21 Apr 2025 S2, 22 Apr 2025 S1, 25 Apr 2025 S1, 25 Apr 2025 S2, 26 Apr 2025 S2. This one: 26 Apr 2025 S2 See all 11 of this type

    128
    The population of towns A and B increase at the rate proportional to their population present at that time. At the end of the year 1984, the population of both the towns was 20,000. At the end of the year 1989, the population of town A was 25,000 and that of town B was 28,000. The difference of populations of towns A and B at the end of 1994 was

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  6. Question 6

    This type asked 10 times: May 2022 S1, 2 May 2023 S1, 11 May 2023 S1, 23 Apr 2025 S1, 25 Apr 2025 S2, 13 Apr 2026 S1, 17 Apr 2026 S1, 19 Apr 2026 S1, 13 May 2026 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 10 of this type

    86
    If the general solution of the differential equation ysec⁡2(xy)dx−(xsec⁡2(xy)−y)dy=0y\sec^2\left(\dfrac{x}{y}\right)dx - \left(x\sec^2\left(\dfrac{x}{y}\right) - y\right)dy = 0 is tan⁡(xy)+g(y)=c\tan\left(\dfrac{x}{y}\right) + g(y) = c, then g(y)=…g(y) = \ldots

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  7. Question 7

    This type asked 9 times: 2 May 2023 S1, 2 May 2023 S2, 3 May 2023 S2, 14 May 2024 S2, 23 Apr 2025 S1, 13 Apr 2026 S2, 16 Apr 2026 S2, 18 Apr 2026 S1, 19 May 2026 S1. This one: 19 May 2026 S1 See all 9 of this type

    87
    A body cools from 100∘C100^\circ\mathrm{C} to 80∘C80^\circ\mathrm{C} in 5 minutes in air at 20∘C20^\circ\mathrm{C}. The time taken to cool from 80∘C80^\circ\mathrm{C} to 60∘C60^\circ\mathrm{C} will be:

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  8. Question 8

    This type asked 8 times: May 2022 S1, 9 May 2024 S1, 10 May 2024 S1, 20 Apr 2025 S2, 25 Apr 2025 S1, 11 Apr 2026 S2, 19 Apr 2026 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 8 of this type

    85
    The differential equation dydx=1−y2y\dfrac{dy}{dx} = \dfrac{\sqrt{1 - y^2}}{y} determines a family of circles with

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  9. Question 9

    This type asked 8 times: 4 May 2023 S1, 9 May 2023 S1, 11 May 2023 S2, 16 May 2023 S1, 14 May 2024 S2, 21 Apr 2025 S2, 25 Apr 2025 S2, 26 Apr 2025 S2. This one: 26 Apr 2025 S2 See all 8 of this type

    118
    The equation of the curve passing through the point (0,2)(0,2) given that the sum of the ordinate and abscissa of any point exceeds the slope of the tangent to the curve at that point by 5 is

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  10. Question 10

    This type asked 7 times: 3 May 2023 S1, 9 May 2024 S2, 10 May 2024 S2, 21 Apr 2025 S2, 23 Apr 2025 S1, 14 May 2026 S1, 14 May 2026 S2. This one: 14 May 2026 S2 See all 7 of this type

    89
    The differential equation of the equation x2+(y−b)2=1x^2 + (y - b)^2 = 1 is

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