Maths · Class 12 · Differential Equations

Differential Equations for JEE

Everything you need for this topic on one page: the ideas, the formulas, the traps, and free lectures that explain it well.

Last updated: 26 October 2026

Direct answer

Order and degree, formation of differential equations, variable separable, homogeneous and linear first-order equations.

Key ideas

Differential Equations: what you must understand

Order = highest derivative; degree = its power after removing radicals
Separate variables when possible
Homogeneous: substitute y = vx
Linear: dy/dx + Py = Q uses an integrating factor

Formula sheet

Must-know formulas for Differential Equations

IF = e^(∫P dx)
Solution: y·IF = ∫Q·IF dx + C
Number of arbitrary constants = order
Exact form: d(xy) = x dy + y dx

One-page formula sheet

Printable Differential Equations formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

Avoid

Common mistakes students make

Degree undefined when derivatives sit inside sin or log
Forgetting the constant before applying initial conditions
Wrong integrating factor sign

For the exam

How this topic is asked in JEE

Appears in almost every JEE Main shift. Linear first-order equations appear almost every shift. Make IF automatic.

Prerequisites: Indefinite Integration.

NCERT map

Where Differential Equations is in NCERT

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

Class	Book	Chapter	Sections JEE asks from
Class 12	Mathematics Part II	Differential Equations	Order and Degree of a Differential Equation; Formation of a Differential Equation; Methods of Solving First Order, First Degree Differential Equations; Differential Equations with Variables Separable; Homogeneous Differential Equations

JEE Advanced level

A JEE Advanced-level example on Differential Equations

Question. Solve the differential equation (x² + y² + 2x)dx + 2y dy = 0, given that y = 1 when x = 0.

Show solution

Rewrite as dy/dx = −(x² + y² + 2x)/(2y). Substitute v = y², so dv/dx = 2y(dy/dx) = −(x² + v + 2x).
This gives the linear equation dv/dx + v = −(x² + 2x). The integrating factor is eˣ.
Multiply through: d/dx(v·eˣ) = −eˣ(x² + 2x). Use the identity ∫eˣ(f + f′)dx = eˣf with f = x².
Integrate: v·eˣ = −eˣ·x² + C, so v = y² = −x² + Ce⁻ˣ.
Apply y(0) = 1: 1 = 0 + C, giving C = 1. The solution is x² + y² = e⁻ˣ.

Answer: x² + y² = e⁻ˣ

This example was solved twice independently and both solutions agree.

Free lectures

Best free lectures for Differential Equations

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

DIFFERENTIAL EQUATIONS in 1 Shot : All Concepts & PYQs Covered || JEE Main & Advanced — JEE Wallah, 7:36:35
Jump to a subtopic (19)
- 00:00 Introduction
- 03:11 Weightage and previous year analysis
- 06:06 Differential equation
- 08:08 Order and Degree of D.E.
- 20:30 Arbitrary constant
- 33:24 Formation of D.E.
- 1:09:37 Solution of D.E.
- 1:14:40 Variable separable form
- 2:03:19 Reducible to variable separable form
- 2:24:08 Homogenous D.E.
- 3:51:33 Reducible to homogeneous D.E.
- 4:06:23 Important form
- 4:20:00 Linear differential equation
- 5:06:00 Reducible to L.D.E.
- 5:22:12 Exact differentials
- 6:15:03 Use of polar coordinates
- 6:30:43 Orthogonal curves
- 6:46:23 Story problems
- 7:33:30 Thank You Bacchon
Differential Equations Class 12 | One Shot | JEE Main & Advanced | Arvind Kalia Sir — JEE Nexus by Unacademy, 3:25:44
Jump to a subtopic (13)
- 0:00 Introduction & Nature of chapter
- 2:54 Index and critical topics
- 5:45 Order and degree of differential equations
- 18:09 Formation of Differential equations
- 40:43 Solution of Differential equations
- 44:13 Solution of First order first degree Differential equations
- 46:34 Variable Separable Method
- 1:08:59 Reducible to variable separable form
- 1:19:16 Homogeneous Differential equations
- 1:59:16 Variable separable form using polar coordinates
- 2:11:02 Linear Differential equations and reducible to LDE
- 2:51:18 Exact form
- 3:09:30 Application of Differential Equations

Practise

Where to practise for free

10 JEE Main 2026 PYQs on Differential Equations, with solutions.
Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
See it move: interactive simulation.

FAQs

Frequently asked questions

Is Differential Equations important for JEE Main 2027?

Appears in almost every JEE Main shift. It is part of the official 'Differential Equations' unit in the JEE Main 2027 syllabus.

What are the most important formulas in Differential Equations?

IF = e^(∫P dx); Solution: y·IF = ∫Q·IF dx + C; Number of arbitrary constants = order.

How should I study Differential Equations for JEE?

Understand the key ideas from NCERT or one full lecture, learn the formula sheet, then solve 25–30 past JEE questions on the topic. Linear first-order equations appear almost every shift. Make IF automatic.