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Differential Equations JEE Main PYQs (2002–2024) with Solutions — Mathematics | JEE Arc

Mathematics

Differential Equations

Appeared 163 times across 23 years of JEE Main papers — about 7.1 questions a year. Every one of them is below, with a full worked solution.

Questions per year

2’02

2’03

2’04

2’05

1’06

1’07

1’08

1’09

1’10

2’11

1’12

1’13

1’14

1’15

3’16

3’17

4’18

16’19

15’20

30’21

30’22

20’23

23’24

234 questions in the bank

Practise this topic

Q01JEE Main 2025April, Unspecified (session-level dataset)MediumDifferential Equations163× since 2002

Let

y=y(x)

be the solution of the differential equation

\frac{dy}{dx} + 3(\tan^2x)\,y + 3y = \sec^2x

, with

y(0)=\tfrac{1}{3}+e^3

. Then

y\bigl(\tfrac{\pi}{4}\bigr)

is equal to:

Q02JEE Main 2025April, Unspecified (session-level dataset)MediumDifferential Equations163× since 2002

If a curve

y=y(x)

passes through the point

(1,\tfrac{\pi}{2})

and satisfies the differential equation

\bigl(7x^4\cot y - e^x\csc y\bigr)\frac{dx}{dy} = x^5

x\ge1

, then at

x=2

, the value of

\cos y

is:

Q03JEE Main 2025April, Unspecified (session-level dataset)MediumDifferential Equations163× since 2002

Let

y = y(x)

be the solution of the differential equation

(x^2 + 1)y' - 2xy = (x^4 + 2x^2 + 1)\cos x

, with

y(0) = 1

. Then

\displaystyle \int_{-3}^{3} y(x)\,dx

is:

Q04JEE Main 2025April, Unspecified (session-level dataset)MediumDifferential Equations163× since 2002

Let

y = y(x)

be the solution curve of the differential equation

x(x^2 + e^x)dy + (e^x(x - 2)y - x^3)dx = 0,\ x > 0

, passing through the point

(1, 0)

. Then

y(2)

is equal to:

Q05JEE Main 2025January, Unspecified (session-level dataset)MediumDifferential Equations163× since 2002

Let a curve

y = f(x)

pass through the points

(0, 5)

and

(\log_e 2, k)

. If the curve satisfies the differential equation

2(3 + y) e^{2x} dx - (7 + e^{2x}) dy = 0

, then

k

is equal to

Q06JEE Main 2025January, Unspecified (session-level dataset)MediumDifferential Equations163× since 2002

x=f(y)

is the solution of the differential equation

\left(1+y^2\right) + \left(x - 2e^{\tan^{-1} y}\right) \frac{dy}{dx} = 0, y \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

with

f(0)=1

, then

f\left(\frac{1}{\sqrt{3}}\right)

is equal to:

Q07JEE Main 2025January, Unspecified (session-level dataset)MediumDifferential Equations163× since 2002

Let

y = y(x)

be the solution of the differential equation

\left(xy - 5x^2 \sqrt{1 + x^2}\right) dx + \left(1 + x^2\right) dy = 0

y(0) = 0

. Then

y(\sqrt{3})

is equal to

Q08JEE Main 2025January, Unspecified (session-level dataset)MediumDifferential Equations163× since 2002

Let

y = y(x)

be the solution of the differential equation

\cos x (\log_e (\cos x))^2 dy + (\sin x - 3y \sin x \log_e (\cos x)) dx = 0, x \in \left(0, \frac{\pi}{2}\right)

. If

y\left(\frac{\pi}{4}\right) = \frac{-1}{\log_e 2}

, then

y\left(\frac{\pi}{6}\right)

is equal to:

Q09JEE Main 2025January, Unspecified (session-level dataset)MediumDifferential Equations163× since 2002

If for the solution curve

y=f(x)

of the differential equation

\frac{dy}{dx}+(\tan x)y=\frac{2+\sec x}{(1+2\sec x)^2}

x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

f\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{10}

, then

f\left(\frac{\pi}{4}\right)

is equal to:

Q10JEE Main 2025January, Unspecified (session-level dataset)MediumDifferential Equations163× since 2002

Let

f : (0, \infty) \to \mathbf{R}

be a function which is differentiable at all points of its domain and satisfies the condition

x^2 f'(x) = 2x f(x) + 3

, with

f(1) = 4

. Then

2 f(2)

is equal to:

Showing the first 10 of 234. Practise this topic or open any question from the full list below.

All 234 Differential Equations questions by year

JEE Main 2026 · 19

JEE Main 2025 · 11

JEE Main 2024 · 37

JEE Main 2023 · 25

JEE Main 2022 · 39

JEE Main 2021 · 42

JEE Main 2020 · 16

JEE Main 2019 · 16

JEE Main 2018 · 4

JEE Main 2017 · 3

JEE Main 2016 · 3

JEE Main 2011 · 2

JEE Main 2010 · 1

Annual Paper 1 · Q3579: Solution of the differential equation cos x dy = y(sin x - y)dx, 0 < x <(π)/2 is:

JEE Main 2009 · 1

Annual Paper 1 · Q3491: The differential equation which represents the family of curves y = c₁e^(c₂x), where c₁, and c₂ are…

JEE Main 2008 · 1

Annual Paper 1 · Q3506: The solution of the differential equation dy/dx = (x + y)/x satisfying the condition y(1)=1 is:

JEE Main 2007 · 1

Annual Paper 1 · Q3490: The differential equation of all circles passing through the origin and having their centres on the x -axis…

JEE Main 2006 · 1

Annual Paper 1 · Q3575: The differential equation whose solution is A x² + B y² = 1 where A and B are arbitrary constants is of

Questions per year

234 questions in the bank

All 234 Differential Equations questions by year

JEE Main 2026 · 19

JEE Main 2025 · 11

JEE Main 2024 · 37

JEE Main 2023 · 25

JEE Main 2022 · 39

JEE Main 2021 · 42

JEE Main 2020 · 16

JEE Main 2019 · 16

JEE Main 2018 · 4

JEE Main 2017 · 3

JEE Main 2016 · 3

JEE Main 2015 · 1

JEE Main 2014 · 1

JEE Main 2013 · 1

JEE Main 2012 · 1

JEE Main 2011 · 2

JEE Main 2010 · 1

JEE Main 2009 · 1

JEE Main 2008 · 1

JEE Main 2007 · 1

JEE Main 2006 · 1

JEE Main 2005 · 2

JEE Main 2004 · 2

JEE Main 2003 · 2

JEE Main 2002 · 2

Questions per year

234 questions in the bank

All 234 Differential Equations questions by year

JEE Main 2026 · 19

JEE Main 2025 · 11

JEE Main 2024 · 37

JEE Main 2023 · 25

JEE Main 2022 · 39

JEE Main 2021 · 42

JEE Main 2020 · 16

JEE Main 2019 · 16

JEE Main 2018 · 4

JEE Main 2017 · 3

JEE Main 2016 · 3

JEE Main 2015 · 1

JEE Main 2014 · 1

JEE Main 2013 · 1

JEE Main 2012 · 1

JEE Main 2011 · 2

JEE Main 2010 · 1

JEE Main 2009 · 1

JEE Main 2008 · 1

JEE Main 2007 · 1

JEE Main 2006 · 1

JEE Main 2005 · 2

JEE Main 2004 · 2

JEE Main 2003 · 2

JEE Main 2002 · 2