Differential Equations JEE Main PYQs PDF, 2020–2026

Differential Equations has 204 questions in JEE Main papers from 2020 to 2026, about 29 per year across all shifts. The free PDF has 202 of them, each with its answer. The most asked topic is Linear Differential Equations (104 questions), followed by Variable Separable Method (70) and Homogeneous Equations (24).

Asked in JEE Main: 2042020–2026, all shifts
In this free PDF: 202with answers
Asked in 2026: 22Latest paper: 2026 Apr S2
Most asked topic: Linear Differential Equations104 Qs · 51% of the chapter
Difficulty mix: 2% easy · 77% medium · 21% hardof the questions in the PDF

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Source: official NTA JEE Main papers · Updated 25 Oct 2026

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7 of this chapter's questions came back in a later paper (2021–2026). See the most repeated.

How often it's asked in JEE Main

Differential Equations had about 1.4 questions per shift in recent JEE Main papers (2024–26). It's one of the most asked Mathematics chapters. Most asked topic: Linear Differential Equations. About 22 questions in the 2026 papers. (Some topics were cut in 2024; see what changed.)

It came up in almost every 2024–26 shift in our bank (about 55 shifts). Question types in 2020–2026: about 147 MCQs and about 57 numerical.

How many questions from Differential Equations in JEE Main, year by year

Year	Questions	Per shift	MCQ	Numerical
2026	22	1.2	16	6
2025	20	1.1	14	6
2024	37	1.9	22	15
2023	27	1.1	20	7
2022	38	1.7	28	10
2021	44	1.7	32	12
2020	16	1.0	15	1
2020–2026	204	1.4	147	57

Most asked Differential Equations topics, 2020–2026

Topic	Questions
Linear Differential Equations	104
Variable Separable Method	70
Homogeneous Equations	24
Order and Degree	6

Counted from PrepWiser's question bank of JEE Main papers, 2020–2026. Per shift = questions that year ÷ shifts in our bank. Updated 25 Oct 2026.

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Two free sheets, made from the past JEE Main questions on this chapter.

Revision notes9 pages, 21 ideas with the usual mistakes.Open the revision notes Formula sheet3 pages, all 22 formulas.Open the formula sheet

Differential Equations questions per year

Year	Asked	In PDF
2026	22	20
2025	20	20
2024	37	37
2023	27	27
2022	38	38
2021	44	44
2020	16	16

in the free PDF asked, not in the PDFThe PDF only has questions we can print in full with a checked answer, so it holds 202 of the 204 asked.

Topic-wise weightage by year

How many Differential Equations questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Topic	Asked	Share	2026	2025	2024	2023	2022	2021	2020
Linear Differential Equations	104	51%	14	17	17	12	19	20	5
Variable Separable Method	70	34%	8	3	13	12	9	17	8
Homogeneous Equations	24	12%	·	·	5	3	9	5	2
Order and Degree	6	3%	·	·	2	·	1	2	1
All topics	204	100%	22	20	37	27	38	44	16

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 20 JEE Main 2026 Differential Equations questions in the free PDF, latest shift first. The 2026 papers asked 22 in all.

JEE Main 2026 · 8 Apr · Shift 2 · Linear Differential Equations

Let $y=y(x)$ be the solution of the differential equation $x\sqrt{1-x^{2}}dy+\left(y\sqrt{1-x^{2}}-x\cos^{{-1}}x\right)dx=0,x\in (0,1),\underset{{x\rightarrow 1^{{-}}}}{lim}y(x)=1$ . Then $y\left(\frac{1}{2}\right)$ equals :

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JEE Main 2026 · 6 Apr · Shift 2 · Linear Differential Equations

Let $f:{\mathbf{R}}\rightarrow {\mathbf{R}}$ be such that $f(xy)=f(x)f(y)$ , for all $x,y\in {\mathbf{R}}$ and $f(0)\neq 0$ . Let $g:[1,\infty)\rightarrow {\mathbf{R}}$ be a differentiable function such that

$x^{2}g(x)=\int_{1}^{x}\left({\mathrm{t}}^{2}f({\mathrm{t}})-\mathrm{tg}({\mathrm{t}})\right)dt$

Then $g(2)$ is equal to :

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JEE Main 2026 · 6 Apr · Shift 1 · Linear Differential Equations

Let $y=y(x)$ be the solution of the differential equation $\left(x^{2}-x\sqrt{x^{2}-1}\right)dy+\left(y\left(x-\sqrt{x^{2}-1}\right)-x\right)dx=0,x\geq 1$ . If $y(1)=1$ , then the greatest integer less than $y(\sqrt{5})$ is $\_\_\_\_$ .
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JEE Main 2026 · 5 Apr · Shift 2 · Linear Differential Equations

Let $f:[1,\infty)\rightarrow {\mathbf{R}}$ be a differentiable function defined as $f(x)=\int_{1}^{x}f({\mathrm{t}}){\mathrm{dt}}+(1-x)(\log_{{{\mathrm{e}}}}x-1)+{\mathrm{e}}$ .

Then the value of $f(f(1))$ is :

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JEE Main 2026 · 5 Apr · Shift 2 · Linear Differential Equations

Let $y=y(x)$ be the solution of the differential equation $(\tan x)^{{1/2}}{\ \mathrm{d}}y=\left(\sec^{3}x-(\tan x)^{{3/2}}y\right){\mathrm{d}}x,0<x<\frac{\pi}{2},y\left(\frac{\pi}{4}\right)=\frac{6\sqrt{2}}{5}$ . If $y\left(\frac{\pi}{3}\right)=\frac{4}{5}\alpha$ , then $\alpha^{4}$ equals

$\_\_\_\_$ .
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JEE Main 2026 · 4 Apr · Shift 2 · Linear Differential Equations

Let $f$ be a twice differentiable function such that

$f(x)=\int_{0}^{x}\tan (t-x)dt-\int_{0}^{x}f(t)\tan tdt,x\in \left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

Then $f^{{''}}\left(\frac{\pi}{6}\right)+12f^{{'}}\left(-\frac{\pi}{6}\right)+f\left(\frac{\pi}{6}\right)$ is equal to _______.
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JEE Main 2026 · 4 Apr · Shift 1 · Variable Separable Method

Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=\left(1+x+x^{2}\right)\left(1-y+y^{2}\right),y(0)=\frac{1}{2}$ . Then $(2y(1)-1)$ is equal to

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JEE Main 2026 · 4 Apr · Shift 2 · Linear Differential Equations

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

$\frac{dy}{dx}+\left(\frac{6x^{2}+\left(3x^{2}+2x^{3}+4\right)e^{{-2x}}}{(x^{3}+2)(2+e^{{-2x}})}\right)y=2+e^{{-2x}}$

$x\in (-1,2)$ , satisfying $y(0)=\frac{3}{2}$ . If $y(1)=\alpha\left(2+e^{{-2}}\right)$ , then $\alpha$ is equal to :

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JEE Main 2026 · 2 Apr · Shift 2 · Variable Separable Method

Let $x=x(y)$ be the solution of the differential equation $2y^{2}\frac{dx}{dy}-2xy+x^{2}=0$ , $y>1$ , $x(e)=e$ .
Then $x(e^{2})$ is equal to:
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JEE Main 2026 · 2 Apr · Shift 1 · Variable Separable Method

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

$(1+\sin x)\frac{dy}{dx}+(y+1)\cos x=0,\ y(0)=0.$ If the curve $y=y(x)$ passes through the point $\left(\alpha,\frac{-1}{2}\right)$ ,

then a value of $\alpha$ is:
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JEE Main 2026 · 2 Apr · Shift 1 · Variable Separable Method

If the curve $y=f(x)$ passes through the point $(1,e)$ and satisfies the differential equation $dy=y(2+\quad log_{e}x)dx$ , $x>0$ , then $f(e)$ is equal to :
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JEE Main 2026 · 28 Jan · Shift 1 · Variable Separable Method

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

$x\frac{dy}{dx}-\sin 2y=x^{3}\left(2-x^{3}\right)\cos^{2}y,x\neq 0.$

If $y(2)=0$ , then $\tan (y(1))$ is equal to

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Sample questions from recent papers

JEE Main 2024 · 9 Apr · Shift 1 · Homogeneous Equations

The solution of the differential equation $(x^2+y^2) \mathrm{d} x-5 x y \mathrm{~d} y=0, y(1)=0$ , is :

(A) $\left|x^2-4 y^2\right|^5=x^2$
(B) $\left|x^2-2 y^2\right|^6=x$
(C) $\left|x^2-2 y^2\right|^5=x^2$
(D) $\left|x^2-4 y^2\right|^6=x$

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Answer: (A)

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JEE Main 2024 · 8 Apr · Shift 1 · Order and Degree

Let $f(x)$ be a positive function such that the area bounded by $y=f(x), y=0$ from $x=0$ to $x=a>0$ is $e^{-a}+4 a^2+a-1$ . Then the differential equation, whose general solution is $y=c_1 f(x)+c_2$ , where $c_1$ and $c_2$ are arbitrary constants, is

(A) $\left(8 e^x+1\right) \frac{d^2 y}{d x^2}-\frac{d y}{d x}=0$
(B) $\left(8 e^x+1\right) \frac{d^2 y}{d x^2}+\frac{d y}{d x}=0$
(C) $\left(8 e^x-1\right) \frac{d^2 y}{d x^2}-\frac{d y}{d x}=0$
(D) $\left(8 e^x-1\right) \frac{d^2 y}{d x^2}+\frac{d y}{d x}=0$

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Answer: (B)

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Frequently asked

How many questions come from Differential Equations in JEE Main?

204 questions from 2020 to 2026, about 29 per year. In 2026 it had 22. The free PDF has 202 of them.

Which Differential Equations topics are most important for JEE Main?

By past papers: Linear Differential Equations (51%), Variable Separable Method (34%) and Homogeneous Equations (12%) of all Differential Equations questions.

Is the Differential Equations PYQ PDF free?

Yes. The PDF and its answer key are free, and you can practise the questions online with no login, with step-by-step solutions where available.

Prefer to solve online? Practise Differential Equations online with step-by-step solutions where available, or work through JEE Main papers shift by shift.

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