Differential Equations

CBSE Class 12 · Mathematics · 31 past questions

1. Q1 2026

   The integrating factor of differential equation $R\frac{dx}{dy} + Px = Q$ where P, Q, R are functions of y is

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2. Q2 2026

   The order and degree of the differential equation $\frac{d}{dx}(e^y) = 0$ respectively are

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3. Q3 2026

   Find the general solution of the following differential equation…

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4. Q4 2026

   The general solution of the differential equation $\frac{dy}{dx}=\frac{\sqrt{y}}{\sqrt{x}}$ is

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5. Q5 2026

   The integrating factor of the differential equation $2x\frac{dy}{dx} - y = 3$ is

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6. Q6 2026

   (a) Solve the following differential equation…

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7. Q7 2026

   Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…

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8. Q8 2025

   Which of the following is not a homogeneous function of $x$ and $y$ ?

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9. Q9 2025

   The integrating factor of differential equation $(x + 2y^3)\frac{dy}{dx} = 2y$ is

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10. Q10 2025

    If p and q are respectively the order and degree of the differential equation…

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11. Q11 2025

    Solve the differential equation $2(y+3) - xy\frac{dy}{dx} = 0$; given $y(1) = -2$.

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12. Q12 2025

    The order and degree of the differential equation…

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13. Q13 2024

    The integrating factor of the differential equation $(1 - x^2)\frac{dy}{dx} + xy = ax$, $-1 < x < 1$, is…

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14. Q14 2024

    The order and degree of the differential equation…

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15. Q15 2024

    Find the particular solution of the differential equation given by…

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16. Q16 2024

    $x \log x \dfrac{dy}{dx} + y = 2 \log x$ is an example of a…

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17. Q17 2024

    A bacteria sample of certain number of bacteria is observed to grow exponentially in a given amount of time.… (with a figure)

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18. Q18 2024

    The differential equation $\frac{dy}{dx}=F(x,y)$ will not be a homogeneous differential equation, if $F(x,y)$…

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19. Q19 2024

    The degree of the differential equation $(y'')^2+(y')^3=x\sin(y')$ is…

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20. Q20 2024

    Find the particular solution of the differential equation given by $2xy + y^2 - 2x^2\frac{dy}{dx} = 0$…

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21. Q21 2023

    The solution of the differential equation $\frac{dx}{x} + \frac{dy}{y} = 0$ is…

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22. Q22 2023

    What is the product of the order and degree of the differential equation…

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23. Q23 2023

    Find the general solution of the differential equation…

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24. Q24 2023

    The sum of the order and the degree of the differential equation…

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25. Q25 2023

    The general solution of the differential equation $x\,dy - (1 + x^2)\,dx = dx$ is…

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26. Q26 2023

    Find the particular solution of the differential equation…

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27. Q27 2023

    Degree of the differential equation $\sin x + \cos\left(\frac{dy}{dx}\right) = y^2$ is

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28. Q28 2023

    The integrating factor of the differential equation…

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29. Q29 2023

    Find the general solution of the differential equation : $(xy - x^2)\,dy = y^2\,dx$.

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30. Q30 2022

    Find the sum of the order and the degree of the differential equation…

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31. Q31 2022

    Find the particular solution of the differential equation $x\frac{dy}{dx}+x\cos^2\left(\frac yx\right)=y$…

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