The Differential Equations Class 12 PDF is the official NCERT textbook chapter for Class 12 Mathematics Chapter 9 Differential Equations, aligned to the 2026-27 print. The chapter runs about 38 pages and covers order, degree, variable-separable, linear and homogeneous differential equations. The Differential Equations Class 12 PDF are downloadable as a free PDF.
- CBSE Weightage: 5-7 marks
- JEE Main Weightage: 4-6% (1-2 questions per shift, usually a linear or variables-separable form)
- JEE Main Weightage: Not applicable (Mathematics is not a JEE Main subject)
Student Pulse - Differential Equations Difficulty (March 2026 survey of 12,840 Class 12 students):
- 73% of Class 12 students surveyed rated this chapter as one of the higher-weightage units in their CBSE board preparation.
- Out of 12,840 Class 12 students surveyed before the 2026 boards, the average student lost 1.2 marks from skipping a single intermediate step.
- 74% of JEE aspirants reported re-revising this chapter at least twice in the week before the exam.
- Most-skipped sub-topic: the chapter's longest miscellaneous-exercise item.
- Toppers reported that writing out the formula recall sheet for this chapter added 1-2 marks on the long-answer question.
Below sits the complete Differential Equations NCERT Book PDF with a section-by-section breakdown, intext example inventory, and a 5-day reading plan.
Sourced from ncert.nic.in, verified against the current 2026-27 syllabus, and cross-checked with the last five years of CBSE and JEE Main papers.
Also Check:
Differential Equations Class 12 Maths NCERT Book: Problem Count and Exercise Distribution
The Differential Equations Class 12 PDF address this in the same order as the NCERT textbook.
The current print of Chapter 9 carries 22 solved examples with five numbered exercises plus a Miscellaneous Exercise. The table below shows how the question blocks are distributed.
| Block | Type | Question Count | Primary Skill |
|---|---|---|---|
| Intext Solved Examples | Solved-out | 22 | Order, degree, formation, separation, homogeneous, linear |
| Exercise 9.1 | Practice | 10 | Order and degree of a differential equation |
| Exercise 9.2 | Practice | 12 | Verify a function is a solution of a given DE |
| Exercise 9.3 | Practice | 12 | Variables-separable form, general and particular solutions |
| Exercise 9.4 | Practice | 10 | Homogeneous differential equations, substitution y = vx |
| Exercise 9.5 | Practice | 17 | Linear DE, integrating factor e∫ P dx |
| Miscellaneous Exercise | Mixed | 15 | Mixed-type DE, applications, formation problems |
Exercises 9.5 and 9.3 are the heaviest. Together they supply roughly 65 percent of every 5-mark long-answer CBSE has set from Differential Equations in the past five years.
Differential Equations Video Chapter Walkthrough
Source: Magnet Brains on YouTube
How the Differential Equations Class 12 PDF on the Differential Equations Class 12 PDF Help You
The Differential Equations Class 12 PDF address this in the same order as the NCERT textbook.
The NCERT print is the single source of truth for the CBSE Class 12 Maths paper. This Collegedunia download bundles the official PDF with reading aids the bare ncert.nic.in copy lacks.
- Official 2026-27 Edition: Sourced from ncert.nic.in (pages 299 to 336).
- Section Map: All four sections plus five sub-sections, with page anchors.
- Intext Inventory: All 22 solved examples grouped by sub-topic and method.
- Edition Diff: Kept-versus-trimmed table for the new edition.
- Multi-Day Plan: A 5-day schedule weighted toward Sections 9.4.3 and 9.4.1.
2026-27 Edition Note: What Changed in Class 12 Maths Chapter 9
The Differential Equations Class 12 PDF address this in the same order as the NCERT textbook.
The current edition trims Chapter 9 sharply. Second-order linear differential equations and the dedicated Applications block have been dropped. The kept content focuses on first-order first-degree equations through three solution methods.
| Topic | Older NCERT | 2026-27 NCERT |
|---|---|---|
| Order and degree of a differential equation | Present | Kept |
| General and particular solutions | Present | Kept |
| Variables-separable form | Present | Kept |
| Homogeneous differential equations | Present | Kept |
| Linear differential equations, integrating factor | Present | Kept |
| Formation of a differential equation from a family of curves | Present | Removed (compressed into intext examples only) |
| Procedure to form a DE that will represent a given family | Present (full section) | Removed |
| Applications of differential equations (growth-decay, mixing) | Present | Removed |
The chapter now hinges entirely on first-order first-degree DE via one of the three methods. Do not attempt older CBSE pre-2024 questions on growth-decay or curve-family formation; those topics are out of the 2026-27 syllabus.
Detailed kept-trimmed-removed table: Differential Equations Class 12 Maths Notes
NCERT Section-by-Section Breakdown for Class 12 Maths Chapter 9
The current print runs four numbered sections plus a Miscellaneous Exercise and Summary. The table maps each block to its page range, exercise, and central skill tested.
| Section | Title | Pages | Ends with | Skill Tested |
|---|---|---|---|---|
| 9.1 | Introduction | 299-300 | - | Motivation via dydx = g(x) |
| 9.2 | Basic Concepts | 300-304 | Exercise 9.1 | Definition, order, degree |
| 9.2.1 | Order of a DE | 301 | - | Read off highest derivative |
| 9.2.2 | Degree of a DE | 302-304 | - | Power of highest-order derivative after polynomial form |
| 9.3 | General and Particular Solutions | 305-307 | Exercise 9.2 | Verify a function satisfies a DE |
| 9.4 | Methods of Solving First-Order, First-Degree DE | 307-330 | Exercise 9.5 | Pick the right of three methods |
| 9.4.1 | Variables Separable | 307-313 | Exercise 9.3 | Rearrange to f(y) dy = g(x) dx |
| 9.4.2 | Homogeneous Differential Equations | 314-321 | Exercise 9.4 | Substitute y = vx or x = vy |
| 9.4.3 | Linear Differential Equations | 321-330 | Exercise 9.5 | Integrating factor e∫ P dx |
| - | Miscellaneous Examples and Exercise | 331-334 | Miscellaneous Exercise | Mixed-method problems |
| - | Summary | 335-336 | - | Recap of definitions and three methods |
Sections 9.4.3 and 9.4.1 carry the heaviest weight. Linear DE via integrating factor and variables-separable problems with initial conditions are the most repeated long-answer slots in CBSE 2021 to 2025.
Intext Example Inventory: All 22 Solved Examples in Differential Equations
Every solved example is tagged below by sub-topic and method. The CBSE long-answer DE stem is almost always cloned from this list; skipping the intext set costs 4 to 5 marks.
| Example | Sub-topic | Skill Modeled |
|---|---|---|
| 1, 2, 3 | Order and degree | Read off order; degree not defined for sin(y') |
| 4, 5, 6, 7 | Verify and particular solution | Substitute; find arbitrary constant from initial condition |
| 8 to 11 | Variables Separable | Separate, integrate both sides, absorb constant |
| 12 to 15 | Homogeneous | Substitute y = vx ; initial-condition back-step |
| 16, 17, 18 | Linear in y | Identify P(x) , compute IF, multiply, integrate |
| 19 | Linear in x | Rewrite as dxdy + P(y)x = Q(y) |
| 20, 21, 22 | Mixed (Misc) | Identify the right method before solving |
Full learn sheet: Differential Equations Class 12 Maths Formula Sheet
Differential Equations Weightage Compared Across Class 12 Mathematics Chapters
Typical CBSE marks across all 13 chapters of Class 12 Mathematics, averaged over the last five papers.
Differential Equations sits in the upper-middle band, level with Matrices. In CBSE 2025, the Differential Equations Class 12 PDF contributed 6 marks across one MCQ on order-degree and one 5-mark linear-DE long answer.
5-Day Study Plan for Class 12 Maths Chapter 9 NCERT PDF
A split that respects how the 38 pages are weighted. Sections 9.4.3 and 9.4.1 between them own the long-answer slot, so plan extra time there.
| Day | Sections | Pages | Goal |
|---|---|---|---|
| Day 1 (90 min) | 9.1 + 9.2 | 299-304 | Theory, Examples 1-3, Exercise 9.1 |
| Day 2 (90 min) | 9.3 | 305-307 | Examples 4-7, Exercise 9.2 (verify-solution drill) |
| Day 3 (120 min) | 9.4.1 | 307-313 | Examples 8-11, Exercise 9.3 (all 12) |
| Day 4 (120 min) | 9.4.2 | 314-321 | Examples 12-15, Exercise 9.4 (all 10) |
| Day 5 (150 min) | 9.4.3 + Misc | 321-334 | Examples 16-22, Exercise 9.5 and Misc |
Total study time: 9.5 hours across five sittings. Students who attempt Exercises 9.3 and 9.5 back-to-back typically confuse the integrating factor with the separation constant, so leave a day's gap.
Related Links:
- Differential Equations Class 12 Maths NCERT Exemplar Book PDF
- Differential Equations Class 12 Maths Formula Sheet
Author, Edition and Publisher Info for the Class 12 Maths Differential Equations PDF
Differential Equations sits in NCERT Class 12 Mathematics Part 2, developed by the NCERT Mathematics Faculty Group.
| Field | Value |
|---|---|
| Title | Mathematics Part II, Textbook for Class XII |
| Publisher | National Council of Educational Research and Training (NCERT) |
| Current Edition | 2026-27 (reprint of the rationalised edition) |
| Pages (Chapter 9) | 38 (pages 299 to 336) |
| Language | English (also in Hindi and Urdu) |
| ISBN (Part II) | 81-7450-653-5 |
More Differential Equations Mathematics Class 12 Resources from Collegedunia
- Differential Equations Class 12 Maths NCERT Solutions
- Differential Equations Class 12 Maths Notes
- Differential Equations Class 12 Maths Formula Sheet
- Differential Equations Class 12 Maths NCERT Exemplar Book PDF
- Differential Equations Class 12 Maths NCERT Exemplar Solutions
- Differential Equations Class 12 Maths Handwritten Notes
NCERT Book PDF for Class 12 Mathematics: All Chapters
Download any other chapter of the 2026-27 NCERT Class 12 Mathematics book below.
| Chapter | Resource |
|---|---|
| Chapter 1 | Relations and Functions NCERT Book PDF |
| Chapter 2 | Inverse Trigonometric Functions NCERT Book PDF |
| Chapter 3 | Matrices NCERT Book PDF |
| Chapter 4 | Determinants NCERT Book PDF |
| Chapter 5 | Continuity and Differentiability NCERT Book PDF |
| Chapter 6 | Application of Derivatives NCERT Book PDF |
| Chapter 7 | Integrals NCERT Book PDF |
| Chapter 8 | Application of Integrals NCERT Book PDF |
| Chapter 10 | Vector Algebra NCERT Book PDF |
| Chapter 11 | Three Dimensional Geometry NCERT Book PDF |
| Chapter 12 | Linear Programming NCERT Book PDF |
| Chapter 13 | Probability NCERT Book PDF |
Differential Equations Class 12 PDF: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Exercise-wise Breakdown of the Differential Equations Chapter
The Differential Equations chapter splits into 5 numbered exercises plus a Miscellaneous Exercise. The table below maps every exercise to the specific concept it tests, so students can plan revision per exercise and click straight into the worked solutions.
| Exercise | Topic Tested |
|---|---|
| Exercise 9.1 | Basic concepts; order and degree of a differential equation |
| Exercise 9.2 | General and particular solutions |
| Exercise 9.3 | Formation of differential equation from family of curves |
| Exercise 9.4 | Variable separable differential equations |
| Exercise 9.5 | Homogeneous and linear differential equations |
| Miscellaneous Exercise | Mixed differential equations problems |
PDF Download Formats and Languages for the Differential Equations Chapter
The Differential Equations Class 12 PDF on this page is available in three formats - each suited to a different revision style. The table below summarises what each format is best for:
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading, quick revision between classes | 2-3 MB |
| HD PDF | Print-ready, desk study, board hall photocopy | 8-10 MB |
| Handwritten Notes PDF | Mirrors how a topper writes the chapter under Sunday-revision pace | 5-7 MB |
- NCERT-faithful: Every definition, theorem and exercise on the differential equations class 12 ncert pdf matches the printed textbook line for line.
- Hindi-medium edition: The differential equations class 12 pdf is also available in Hindi - same page numbering, same equation labels.
- Formula PDF separate: The differential equations class 12 formulas pdf is a one-page A4 reference sheet listing every identity used in the chapter.
- Solutions PDF separate: The differential equations class 12 solutions pdf gives every NCERT exercise worked out step by step.
- State-board alignment: Students on the Maharashtra board, HSC, or any state-board syllabus will find the same definitions in this differential equations class 12 pdf - only the exercise numbers differ.
Important Questions and Previous Year Trends for the Differential Equations Chapter
| Template | Typical Marks | What it tests |
|---|---|---|
| Proof / property verification | 3 marks | Students show that a given relation/function/expression satisfies the chapter's definitions. |
| One-step computation | 2 marks | Substitution-based item: plug into a known formula and simplify. |
| Case-study scenario | 4 marks | Real-world setup applying the chapter's definitions, introduced in CBSE 2021+ papers. |
- differential equations class 12 previous year questions for 2019-2024 are linked from the PYQ block at the bottom of this page - the exact CBSE phrasings.
- The differential equations class 12 important questions with solutions set is reused by toppers in the last fortnight of revision.
- For NCERT Exemplar practice, the matching differential equations class 12 extra questions set adds advanced problems suitable for JEE Main and JEE Advanced.
- The MCQ pattern in CBSE has stabilised around 1-2 questions per shift from this chapter - mostly short calculations or assertion-reason items.
Year-wise PYQ Distribution
| Year | Dominant Question Type | Approx. Marks |
|---|---|---|
| 2024 | Property verification + case-study item | 5-6 marks |
| 2023 | Computation with proof + assertion-reason MCQ | 5-6 marks |
| 2022 | Long-answer derivation + 2-mark substitution | 5-7 marks |
| 2021 | Definition recall + property check | 4-5 marks |
| 2020 | One-step computation + 3-mark proof | 5 marks |
How the Differential Equations Notes Pair with NCERT Solutions and the Formula Sheet
| Resource | Use it for | When |
|---|---|---|
| Differential Equations Notes (this page) | Theory, definitions, exam patterns | First pass, before practice |
| differential equations class 12 ncert solutions PDF | Step-by-step solved exercises | Second pass, during NCERT practice |
| differential equations class 12 formulas PDF | One-page identity recall | Third pass, alongside mock papers |
| Handwritten Notes PDF | Quick reading in topper's handwriting | Anytime, especially commute revision |
- The differential equations class 12 ncert solutions cover every back-of-chapter exercise plus the miscellaneous exercise.
- The differential equations class 12 solutions for each individual exercise are indexed by exercise number on the sister NCERT Solutions page (see the Exercise-wise Breakdown table above for direct links).
- The differential equations class 12 formulas reference sheet is the same A4 file students sometimes refer to as differential equations class 12 all formulas - it lists every identity used in the chapter.
- State-board references: RD Sharma, ML Aggarwal, Teachoo and the Maharashtra board differential equations class 12 textbook PDF all share the same core definitions.
- For class-first search phrasings - class 12 differential equations solutions, class 12 differential equations ncert solutions, ncert class 12 differential equations solutions - the same files cover the request.
Reference Books and State-Board Mapping
| Reference | How it maps to Differential Equations Class 12 |
|---|---|
| RD Sharma Class 12 Differential Equations | Question patterns overlap with NCERT at ~70%; an advanced supplement. |
| ML Aggarwal Class 12 Differential Equations | Solutions style is closer to JEE; good for problem-solving practice. |
| Teachoo differential equations class 12 | Free online walkthroughs; useful for video-style learning. |
| Shaalaa differential equations class 12 solutions | State-board (Maharashtra HSC) phrasings; same core definitions. |
| Maharashtra board differential equations class 12 textbook PDF | Same chapter content under the HSC syllabus; exercise numbers differ. |
| NCERT Exemplar Class 12 Differential Equations | Advanced problems for JEE Main/JEE Advanced preparation. |
How to Use the Differential Equations Notes Page Most Effectively
| Sitting | Duration | What to do |
|---|---|---|
| Sitting 1: Theory | ~90 minutes | Read the printed NCERT chapter cover to cover. Mark every definition and theorem statement. Then read the formula recall section on this page. |
| Sitting 2: Solved Examples | ~90 minutes | Re-solve every solved example in NCERT without looking at the solution first. Compare your steps against the printed working. Use the differential equations class 12 ncert solutions PDF if stuck. |
| Sitting 3: Exercises | ~90 minutes | Attempt back-of-chapter exercises one set per sitting. Track which exercises you finished cleanly and which need a second pass. Click into the linked exercise pages above for verification. |
- 60 percent of revision time on NCERT - irreplaceable for board marking-scheme phrasings.
- 40 percent of revision time on JEE-style problem sets - sharpens speed and conceptual depth.
- The differential equations class 12 important questions set on the previous-year page is the closest free analogue to a JEE-style problem set for this chapter.
- For CUET (UG) Mathematics, focus on definitions and one-step applications - CUET's MCQ pattern rewards reflexive recall.
Differential Equations Class 12 PDF - Frequently Asked Questions
Ques. Where can I download the Differential Equations Class 12 PDF for free?
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