The curve amongst the family of curves represented by the differential equation, (x 2 – y 2 )dx + 2xy dy = 0 which passes through (1, 1) is :

a circle with centre on the x-axis

a circle with centre on the y-axis

an ellipse with major axis along the y-axis

a hyperbola with transverse axis along the x-axis

Differential Equations — JEE Main Previous Year Questions

213 solved PYQs · 2016–2026 · Mathematics

Solved PYQs: 213
Years covered: 2016–2026
Avg / year: ~19
Subject: Mathematics

How many JEE Main questions come from Differential Equations?

Differential Equations has contributed 213 questions to Joint Entrance Examination (Main) papers between 2016 and 2026 — an average of about 19 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 213 questions carries a written, step-by-step solution, and each is tagged to Differential Equations within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Differential Equations questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 213 Differential Equations questions (with full written solutions) are available in practice.

Question 1 · JEE Main 2021
Let y(x) be the solution of the differential equation 2x^2 dy + (e^y - 2x)dx = 0, x > 0. If y(e) = 1, then y(1) is equal to :
1. (A) $0$
2. (B) $2$
3. (C) $lo g_{e} 2$
4. (D) $lo g_{e} (2 e)$
Show answerAnswer
$Answer: (C) lo g_{e} 2$
Question 2 · JEE Main 2021
Let us consider a curve, y = f(x) passing through the point (-2, 2) and the slope of the tangent to the curve at any point (x, f(x)) is given by f(x) + xf'(x) = x² . Then :
1. (A) $x^{2} + 2 x f (x) - 12 = 0$
2. (B) $x^{3} + x f (x) + 12 = 0$
3. (C) $x^{3} - 3 x f (x) - 4 = 0$
4. (D) $x^{2} + 2 x f (x) + 4 = 0$
Show answerAnswer
$Answer: (C) x^{3} - 3 x f (x) - 4 = 0$
Question 3 · JEE Main 2020
If x 3 dy + xy dx = x 2 dy + 2y dx; y(2) = e and x > 1, then y(4) is equal to :
1. (A) $\frac{e}{2}$
2. (B) $\frac{1}{2} + e$
3. (C) $\frac{3}{2} + e$
4. (D) $\frac{3}{2} e$
Show answerAnswer
$Answer: (D) \frac{3}{2} e$
Question 4 · JEE Main 2019
The curve amongst the family of curves represented by the differential equation, (x 2 – y 2 )dx + 2xy dy = 0 which passes through (1, 1) is :
1. (A) $a circle with centre on the y-axis$
2. (B) $an ellipse with major axis along the y-axis$
3. (C) $a circle with centre on the x-axis$
4. (D) $a hyperbola with transverse axis along the x-axis$
Show answerAnswer
$Answer: (C) a circle with centre on the x-axis$
Question 5 · JEE Main 2018
The curve satisfying the differential equation, (x^2 - y^2) dx + 2xydy = 0 and passing through the point (1, 1) is :
1. (A) $a circle of radius one.$
2. (B) $a hyperbola.$
3. (C) $an ellipse.$
4. (D) $a circle of radius two.$
Show answerAnswer
$Answer: (A) a circle of radius one.$

Differential Equations questions by year

Year	Questions	Share of chapter questions
2026	21
2025	21
2024	37
2023	24
2022	34
2021	37
2020	14
2019	16
2018	3
2017	3
2016	3

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FAQs

How many JEE Main questions have been asked from Differential Equations?

EByAi's bank holds 213 real JEE Main questions from Differential Equations, asked between 2016 and 2026 — about 19 per year on average. Every count is measured from actual papers, not estimated.

Is Differential Equations important for JEE Main?

213 questions over 11 papers make Differential Equations a high-weightage chapter in JEE Main Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Differential Equations PYQs online for free?

Yes. EByAi lets you solve JEE Main past-year questions in the browser with written solutions — free daily practice, no card needed.

More JEE Main Mathematics chapters

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