Differential Equations

Bihar Board Class 12 · Mathematics · 47 past questions

1. Q1 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2024 Set J2024 Set D201720162015

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

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2. Q2 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   The integrating factor of the differential equation $(1+x^2)\frac{dy}{dx} + y = e^{\tan^{-1}x}$ is

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3. Q3 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

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

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4. Q4 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   The order and degree of the differential equation…

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5. Q5 2025

   Degree of the differential Equation…

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6. Q6 2025

   Integrating factor of the differential Equation $\dfrac{dy}{dx} + y\log x = \cos x$ is

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7. Q7 2025

   Solution of Differential equation $y\log y\,dx - x\,dy = 0$ is

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8. Q8 2025

   Solution of differential equation $\dfrac{dy}{dx} = \dfrac{1+y^{2}}{1+x^{2}}$ is

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9. Q9 2025

   Integrating factor of differential equation $\dfrac{dx}{dy}+3x=e^{2y}$ is

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10. Q10 2025

    Find the integrating factor of the differential equation $(1-x^2)\dfrac{dy}{dx}-xy=1$.

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11. Q11 2025

    Solve: $\frac{dy}{dx} + y = e^{-x}$

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12. Q12 2025

    Solve: $(1+\tan y)(dx-dy)+2x\,dy=0$

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13. Q13 2024 Set D2024 Set J

    The order and degree of the differential equation…

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14. Q14 2024 Set D2024 Set J

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

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15. Q15 2024 Set D2024 Set J

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

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16. Q16 2024 Set J20232023 Set E

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

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17. Q17 2023

    The solution of the differential equation $x^2\,dx + y^2\,dy = 0$ is

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18. Q18 2023

    The solution of the differential equation $e^{3x}\,dx + e^{4y}\,dy = 0$ is

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19. Q19 20232023 Set E

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

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20. Q20 20232023 Set E

    The solution of the differential equation dx + dy = 0 is

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21. Q21 20232023 Set E

    The integrating factor of the differential equation $\dfrac{dy}{dx}+\dfrac{2y}{x}=5x^2$ is

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22. Q22 2023 Set E

    The solution of the differential equation $x^2dx+y^2dy=0$ is

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23. Q23 2023 Set E

    The solution of the differential equation $e^{3x}dx+e^{4y}dy=0$ is

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24. Q24 2021 Set J2021 Set I

    The order of the differential equation…

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25. Q25 2021 Set J2021 Set I

    Solution of the differential equation $x\,dy + y\,dx = 0$ is

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26. Q26 2021 Set J2021 Set I

    Solution of the differential equation $\frac{y\,dx - x\,dy}{y^2} = 0$ is

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27. Q27 2021 Set J2021 Set I

    Integrating factor of the differential equation $\frac{dy}{dx} + Py = Q$ is

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28. Q28 2019 Set F

    Integrating factor of the differential equation $\frac{dy}{dx} + y\sec x = \tan x$ is -

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29. Q29 2019 Set F

    Integrating factor (I.F) of the differential equation $\frac{dy}{dx} - y\cos x = \sin x\cos x$ is -

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30. Q30 2019 Set F2015

    The order of the differential equation $\dfrac{d^2y}{dx^2} + x^3\left(\dfrac{dy}{dx}\right)^3 = x^4$ is

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31. Q31 2019 Set F

    Which of the following is a homogeneous differential equation?

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32. Q32 2018

    The differential equation $1 + \left(\frac{dy}{dx}\right)^2 = \left(\frac{d^2y}{dx^2}\right)^3$ is of order…

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33. Q33 2018

    solution of the differential equation $y\,dx - x\,dy = xy\,dx$ is

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34. Q34 2018

    Integrating factor (I.F) of differential equation $\frac{dy}{dx} + \frac{y}{x} = \frac{y^2}{x^2}$ is

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35. Q35 2018

    solution of $\frac{x\,dy - y\,dx}{x^2 + y^2} = 0$ is…

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36. Q36 2018

    Solve: $(x^2-y^2)\dfrac{dy}{dx}=2xy$

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37. Q37 2018

    Evaluate $x\cos x\dfrac{dy}{dx}+y(x\sin x+\cos x)=1$

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38. Q38 2017

    The solution of $\frac{dy}{dx} = \frac{x}{y}$ is-

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39. Q39 2017

    The order of the differential equation $\frac{dy}{dx} + 4y = 2x$ is-

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40. Q40 2017

    The degree of the equation $\left(\frac{d_2 y}{dx^2}\right)^3 - 4\frac{dy}{dx} = 2$ is

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41. Q41 2017

    Solve $\frac{dy}{dx} - \frac{xy}{1 - x^2} = \frac{1}{1 - x^2}$.

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42. Q42 2016

    The integrating factor of the linear differential equation $\frac{dy}{dx}+Py=0$

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43. Q43 2016

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

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44. Q44 2016

    The degree of the equation $\left(\frac{d^2y}{dx^2}\right)^2-x\left(\frac{dy}{dx}\right)^3=y^3$ is

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45. Q45 2015

    The integrating factor of the linear differential equation $\dfrac{dy}{dx} = y\tan x\sec^2 x$

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46. Q46 2015

    The degree of the differential equation $1 + \left(\dfrac{dy}{dx}\right)^2 = \dfrac{d^2y}{dx^2}$ is

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47. Q47 2015

    Solve the differential equation: $(x-y)\,dy-(x+y)\,dx=0$

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