PrepWiser. Practise online

Differential Equations JEE Main PYQs, 2020 to 2025

Differential Equations has 174 questions in JEE Main papers from 2020 to 2025, about 29 per year across all shifts. The most asked topic is Linear Differential Equations (89 questions), followed by Variable Separable Method (58) and Homogeneous Equations (23).

Updated

Download free PDF (174 questions + answer key, 0.6 MB) Practise online, free, no login
174Total PYQs
6Years covered
4Topics
2025 Apr S2Latest paper

Differential Equations questions per year

YearQuestions
202520
202435
202326
202236
202141
202016

Topic-wise weightage

TopicQuestionsShare of chapterLast asked
Linear Differential Equations8951%2025
Variable Separable Method5834%2025
Homogeneous Equations2313%2024
Order and Degree42%2024

Sample questions from recent papers

JEE Main 2025 · 8 Apr · Shift 2 · Linear Differential Equations

Let f(x)=x−1f(x) = x - 1 and g(x)=exg(x) = e^x for x∈Rx \in \mathbb{R}. If dydx=(e−2xg(f(f(x)))−yx)\frac{dy}{dx} = \left( e^{-2\sqrt{x}} g\left(f(f(x))\right) - \frac{y}{\sqrt{x}} \right), y(0)=0y(0) = 0, then y(1)y(1) is

  1. (A)

    1−e3e4\frac{1 - e^3}{e^4}

  2. (B)

    e−1e4\frac{e-1}{e^4}

  3. (C)

    1−e2e4\frac{1 - e^2}{e^4}

  4. (D)

    2e−1e3\frac{2e - 1}{e^3}

Answer: (B)

Step-by-step solution

JEE Main 2025 · 24 Jan · Shift 1 · Variable Separable Method

Let y=y(x)\mathrm{y}=\mathrm{y}(\mathrm{x}) be the solution of the differential equation (xy−5x21+x2)dx+(1+x2)dy=0,y(0)=0\left(x y-5 x^2 \sqrt{1+x^2}\right) d x+\left(1+x^2\right) d y=0, y(0)=0. Then y(3)y(\sqrt{3}) is equal to

  1. (A)532\frac{5 \sqrt{3}}{2}
  2. (B)152\sqrt{\frac{15}{2}}
  3. (C)143\sqrt{\frac{14}{3}}
  4. (D)222 \sqrt{2}

Answer: (A)

Step-by-step solution

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

The solution of the differential equation (x2+y2)dx−5xy dy=0,y(1)=0(x^2+y^2) \mathrm{d} x-5 x y \mathrm{~d} y=0, y(1)=0, is :

  1. (A)∣x2−4y2∣5=x2\left|x^2-4 y^2\right|^5=x^2
  2. (B)∣x2−2y2∣6=x\left|x^2-2 y^2\right|^6=x
  3. (C)∣x2−2y2∣5=x2\left|x^2-2 y^2\right|^5=x^2
  4. (D)∣x2−4y2∣6=x\left|x^2-4 y^2\right|^6=x

Answer: (A)

Step-by-step solution

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

Let f(x)f(x) be a positive function such that the area bounded by y=f(x),y=0y=f(x), y=0 from x=0x=0 to x=a>0x=a>0 is e−a+4a2+a−1e^{-a}+4 a^2+a-1. Then the differential equation, whose general solution is y=c1f(x)+c2y=c_1 f(x)+c_2, where c1c_1 and c2c_2 are arbitrary constants, is

  1. (A)(8ex+1)d2ydx2−dydx=0\left(8 e^x+1\right) \frac{d^2 y}{d x^2}-\frac{d y}{d x}=0
  2. (B)(8ex+1)d2ydx2+dydx=0\left(8 e^x+1\right) \frac{d^2 y}{d x^2}+\frac{d y}{d x}=0
  3. (C)(8ex−1)d2ydx2−dydx=0\left(8 e^x-1\right) \frac{d^2 y}{d x^2}-\frac{d y}{d x}=0
  4. (D)(8ex−1)d2ydx2+dydx=0\left(8 e^x-1\right) \frac{d^2 y}{d x^2}+\frac{d y}{d x}=0

Answer: (B)

Step-by-step solution

All 174 questions are in the free PDF above, grouped by topic.

Frequently asked

How many questions come from Differential Equations in JEE Main?

174 questions from 2020 to 2025, about 29 per year. In 2025 it had 20.

Which Differential Equations topics are most important for JEE Main?

By past papers: Linear Differential Equations (51%), Variable Separable Method (34%) and Homogeneous Equations (13%) of all Differential Equations questions.

Is the Differential Equations PYQ PDF free?

Yes. The PDF, the answer key and every step-by-step solution on PrepWiser are free, with no login needed to practise.

More Mathematics chapters

JEE Main PYQs by year: 2025 · 2024 · 2023 · 2022 · 2021 · 2020

Answers follow NTA's final answer keys. Typing errors are possible, so check doubtful answers against the official key. Spotted a mistake? prepwiser.in/feedback · Terms: prepwiser.in/terms