Differential Equations

JEE Advanced · Mathematics · 31 past questions

1. Q1 2026 Paper 2

   Let $y:(-\infty,\infty)\to(0,\infty)$ be the solution of the differential equation…

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2. Q2 2026 Paper 2

   Let $y=f(x)$ be the real valued function defined on the interval $(0,\infty)$, satisfying $y(1)=0$ and the…

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3. Q3 2025 Paper 1

   For all $x>0$, let $y_1(x)$, $y_2(x)$, and $y_3(x)$ be the functions satisfying…

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4. Q4 2025 Paper 2

   Let $y(x)$ be the solution of the differential equation…

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5. Q5 2024 Paper 1

   Let $f(x)$ be a continuously differentiable function on the interval $(0,\infty)$ such that $f(1)=2$ and…

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6. Q6 2023 Paper 2

   Let $f:[1,\infty)\to\mathbb{R}$ be a differentiable function such that $f(1)=\frac{1}{3}$ and…

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7. Q7 2023 Paper 2

   For $x \in \mathbb{R}$, let $y(x)$ be a solution of the differential equation…

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8. Q8 2022 Paper 2

   If $y(x)$ is the solution of the differential equation…

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9. Q9 2022 Paper 2

   For $x \in \mathbb{R}$, let the function $y(x)$ be the solution of the differential equation…

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10. Q10 2021 Paper 2

    For any real numbers $\alpha$ and $\beta$, let $y_{\alpha,\beta}(x),\ x\in\mathbb{R}$, be the solution of the…

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11. Q11 2020 Paper 2

    Let $b$ be a nonzero real number. Suppose $f:\mathbb{R}\to\mathbb{R}$ is a differentiable function such that…

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12. Q12 2019 Paper 1

    Let $\Gamma$ denote a curve $y=y(x)$ which is in the first quadrant and let the point $(1,0)$ lie on it. Let…

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13. Q13 2018 Paper 1

    Let $f: \mathbb{R} \to \mathbb{R}$ and $g: \mathbb{R} \to \mathbb{R}$ be two non-constant differentiable…

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14. Q14 2018 Paper 2

    Let $f:\mathbb{R}\to\mathbb{R}$ be a differentiable function with $f(0)=0$. If $y=f(x)$ satisfies the…

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15. Q15 2017 Paper 2

    If $y = y(x)$ satisfies the differential equation…

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16. Q16 2016 Paper 1

    Let $f:(0,\infty)\to\mathbb{R}$ be a differentiable function such that $f'(x)=2-\dfrac{f(x)}{x}$ for all…

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17. Q17 2016 Paper 1

    A solution curve of the differential equation $(x^2+xy+4x+2y+4)\dfrac{dy}{dx}-y^2=0$, $x>0$, passes through…

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18. Q18 2015 Paper 1

    Let $y(x)$ be a solution of the differential equation $(1+e^x)y' + ye^x = 1$. If $y(0)=2$, then which of the…

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19. Q19 2015 Paper 1

    Consider the family of all circles whose centers lie on the straight line $y = x$. If this family of circles…

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20. Q20 2014 Paper 2

    The function $y = f(x)$ is the solution of the differential equation…

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21. Q21 2013 Paper 1

    A curve passes through the point $\left(1, \frac{\pi}{6}\right)$. Let the slope of the curve at each point…

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22. Q22 2012 Paper 1

    If $y(x)$ satisfies the differential equation $y'-y\tan x=2x\sec x$ and $y(0)=0$, then

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23. Q23 2011 Paper 1

    Let $f : [1, \infty) \to [2, \infty)$ be a differentiable function such that $f(1) = 2$. If…

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24. Q24 2011 Paper 2

    Let $y'(x)+y(x)g'(x)=g(x)g'(x)$, $y(0)=0$, $x\in\mathbb{R}$, where $f'(x)$ denotes $\dfrac{d\,f(x)}{dx}$ and…

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25. Q25 2010 Paper 1

    Let $f$ be a real-valued differentiable function on $\mathbf{R}$ (the set of all real numbers) such that…

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26. Q26 2009 Paper 1

    Let $f$ be a non-negative function defined on the interval $[0,1]$. If…

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27. Q27 2009 Paper 1

    Match the statements/expressions in Column I with the open intervals in Column II.

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28. Q28 2009 Paper 2

    Let $f:\mathbf{R}\to\mathbf{R}$ be a continuous function which satisfies…

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29. Q29 2008 Paper 2

    Let a solution $y=y(x)$ of the differential equation…

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30. Q30 2007 Paper 1

    Let $f(x)$ be differentiable on the interval $(0,\infty)$ such that $f(1)=1$, and…

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31. Q31 2007 Paper 2

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

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