The NCERT Exemplar Class 12 Maths Differential Equations provide the official NCERT Exemplar problem set for Class 12 Mathematics Chapter 9 Differential Equations. The booklet sits above the NCERT Exemplar Class 12 Maths Differential Equations exercises in difficulty and is the standard source of higher-order practice. The booklet is free to download as a single PDF.
| Quick Fact | Value |
|---|---|
| Total problems | 114 (24 solved + 90 exercise) |
| MCQ block (JEE-style) | 30 problems |
| LA block (CBSE 5-mark) | 20 problems |
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.
Of all thirteen Class 12 Mathematics chapters, this is the only one whose Exemplar density maps one-to-one to JEE Main MCQ shifts since 2022. Collegedunia tags each problem by solution method.
the NCERT Exemplar Class 12 Maths Differential Equations is the official NCERT Exemplar print with method tags added in the margin.
Also Check:
NCERT Maths Exemplar Class 12 PDF Download Chapter 9 Differential Equations: What You Get
The NCERT Exemplar Class 12 Maths Differential Equations address this in the same order as the NCERT textbook.
The Exemplar print is a brief theory recap followed by a graded problem set running from order-and-degree drills to multi-step linear equations. The table below maps each problem range to its method and pages.
| Section | Range | Pages | Covers |
|---|---|---|---|
| 9.1 Overview | 9 points | 1-3 | Order, degree, three methods, integrating factor |
| Solved Examples: SA | Ex 1 to Ex 12 | 3-9 | Order, degree, formation, variable separable, homogeneous |
| Solved Examples: LA + MCQ | Ex 13 to Ex 24 | 9-13 | Linear equations, mixed-method, single-correct MCQs |
| Exercise: SA | Q1 to Q26 | 13-17 | Method-mix, formation from family of curves |
| Exercise: LA | Q27 to Q46 | 17-19 | Linear and homogeneous LA, particular solutions |
| Exercise: Objective (MCQ) | Q47 to Q76 | 19-23 | Order, degree, method recognition, integrating factor |
| Exercise: Fill-in + True or False | Q77 to Q90+ | 23-25 | Recall fill-ins and conceptual statements |
Pages 1 to 3 are short enough for morning revision; the heavy lifting starts at page 13, where the Exemplar shifts from method modelling to method recognition.
Differential Equations NCERT Exemplar Video Walkthrough
Source: Class 12 PCMB on YouTube
How the NCERT Exemplar Class 12 Maths Differential Equations on the NCERT Exemplar Class 12 Maths Differential Equations Help You
The bare Exemplar is a problem book with no method tagging and no cross-reference to the NCERT Exemplar Class 12 Maths Differential Equations. The Collegedunia download adds the prep aids both CBSE and JEE Main candidates ask for after their first attempt.
- Method tags on every problem, sorted as variable separable, homogeneous, linear in y, linear in x or formation.
- Integrating-factor quick card with the three standard IF forms and derivations on one page.
- Order-and-degree trap list covering the 8 patterns where the answer is "degree not defined".
- JEE Main recurrence map showing which Exemplar MCQs have been recycled in JEE Main shifts since 2022.
Question-Type Distribution in the Class 12 Maths Chapter 9 Exemplar
The NCERT Exemplar Class 12 Maths Differential Equations address this in the same order as the NCERT textbook.
The Exemplar splits Chapter 9 across four formats. CBSE-prep should prioritise SA and LA; JEE aspirants should drill the MCQ block under timed conditions.
| Type | Count | Marks Each | Total Marks | Best For |
|---|---|---|---|---|
| Solved Examples | 24 | - | - | Method modelling |
| Short Answer (SA) | 26 | 2-4 | ~78 | CBSE SA Section |
| Long Answer (LA) | 20 | 5-6 | ~110 | CBSE 5-mark LA |
| MCQ (Objective Type) | 30 | 1 | 30 | JEE Main and CBSE MCQ |
| True or False | 14 | 1 | 14 | CBSE Section A |
Why the NCERT Exemplar Matters for Differential Equations Preparation
The NCERT Exemplar Class 12 Maths Differential Equations address this in the same order as the NCERT textbook.
The Chapter 9 textbook carries roughly 95 problems across 5 exercises and the Miscellaneous Exercise. The Exemplar adds about 90 more, but nearly half is single-correct MCQ (the JEE Main format), with the rest split between LA and True or False (the CBSE pattern).
- Order and Degree drills: 12 problems on order and degree identification, including the "degree not defined" trap when the equation is not polynomial in derivatives.
- Three solution methods side by side: variable separable, homogeneous and linear problems are interleaved, forcing method recognition under exam pressure.
- Formation of differential equations: over 15 problems train the eliminate-the-arbitrary-constants skill CBSE has used on 4 of the last 5 board papers.
Exemplar vs NCERT Textbook Difficulty for Differential Equations
The textbook drills one method per exercise and labels it in the heading. The Exemplar mixes methods inside the same exercise, demanding method recognition before solving.
| Concept | NCERT Textbook Style | NCERT Exemplar Style |
|---|---|---|
| Order and Degree | d2ydx2 + 3dydx + 2y = 0 . | √dydx - 4dydx - 7x = 0 ; state whether degree is defined. |
| Variable Separable | Solve dydx = (1 + x2)(1 + y2) . | Solve dydx = cos(x + y) using v = x + y , then separate. |
| Homogeneous | Solve (x2 + y2)dx + 2xy dy = 0 using y = vx . | Solve y dx + xlogyx dy - 2x dy = 0 ; identify as homogeneous first. |
| Linear Equation | Solve dydx + 2y = sin x . | Solve (1 + y2) dx = (tan-1y - x) dy ; linear in x, IF = etan-1y . |
| Formation | Form the equation for y = acos x + bsin x . | Form the equation of the family of circles touching the x-axis at the origin. |
The Exemplar always asks you to first identify the method, then solve. Textbook-only students lose 1 to 2 marks on every CBSE 5-mark LA because Boards now copy this layer.
Full learn sheet: Differential Equations Class 12 Maths NCERT Exemplar Solutions
JEE Main Prep Value of the Class 12 Maths Differential Equations Exemplar
Differential Equations is a top-three highest-yield JEE Main chapter. Almost every shift since 2022 has carried 2 to 3 questions, and the Exemplar MCQs are calibrated to that pattern.
| JEE Main Question Pattern | Matching Exemplar Problem | Why It Trains the Pattern |
|---|---|---|
| Identify order or degree | Q47, Q48, Q53, Ex 14 | "Degree not defined" trap |
| IF for a linear equation | Q57, Q62, Q71, Ex 19 | Direct e∫ P dx recall |
| Variable-separable MCQ | Q54, Q60, Q73, Q75 | Separation, log, sign tracking |
| Homogeneous MCQ | Q63, Q68, Ex 16 | Speed drill on y = vx |
| Formation from family of curves | Q49, Q55, Q66 | Mirrors JEE Main 2023 and 2024 shifts |
2026-27 Syllabus Alignment for the Chapter 9 Exemplar
The Exemplar was not revised in the 2022-23 update, but the Chapter 9 textbook changed in one place: the exact-equation method, earlier an extra unit, was removed. The Exemplar still keeps a few exact-form problems that CBSE-only students can skip.
| Topic | In 2026-27 Textbook? | In Exemplar PDF? | Should You Solve? |
|---|---|---|---|
| Order and Degree | Yes | Yes | Priority 1 |
| Formation | Yes | Yes | Priority 1 |
| Variable Separable | Yes | Yes | Yes |
| Homogeneous | Yes | Yes | Yes |
| Linear (IF) | Yes | Yes | Yes, esp. JEE |
| Exact Equations | Removed | Few | Skip CBSE; optional JEE |
Roughly 5% of Exemplar problems rely on the exact-equation method dropped from the 2026-27 textbook. CBSE-only students should skip these; JEE aspirants can pick them up later.
Detailed kept-trimmed-removed table: Differential Equations Class 12 Maths NCERT Book PDF
Five-Day Parallel-Track Plan with the Textbook and the Exemplar
The Exemplar is not a replacement for the NCERT Exemplar Class 12 Maths Differential Equations; it is the calibration layer on top of it. Interleave the two: read a section, finish the NCERT Exemplar Class 12 Maths Differential Equations exercise, then attempt Exemplar problems on the same method.
- Day 1 (Order, Degree, Formation): Read Sections 9.1 to 9.3; attempt Exemplar SA Q1 to Q8 plus Examples 1 to 5 in 90 minutes.
- Day 2 (Variable Separable): Finish Exercise 9.3; attempt Exemplar SA Q9 to Q15 plus LA Q27 to Q30 under a 75-minute timer.
- Day 3 (Homogeneous): Revise the y = vx substitution; attempt LA Q31 to Q36 plus Examples 14 to 17 in 90 minutes.
- Day 4 (Linear): Drill the integrating-factor method; attempt LA Q37 to Q46 plus Examples 18 to 21 back to back.
- Day 5 (Objective): MCQs Q47 to Q76 plus True or False Q83 to Q90 at 90 seconds per item for JEE Main calibration.
Related Links:
More Differential Equations Class 12 Maths Resources
NCERT Exemplar Book PDF for Class 12 Mathematics: All Chapters
Download any other Class 12 Maths chapter's Exemplar PDF below.
| Chapter | Exemplar Book PDF |
|---|---|
| Chapter 1 | Relations and Functions Exemplar PDF |
| Chapter 2 | Inverse Trigonometric Functions Exemplar PDF |
| Chapter 3 | Matrices Exemplar PDF |
| Chapter 4 | Determinants Exemplar PDF |
| Chapter 5 | Continuity and Differentiability Exemplar PDF |
| Chapter 6 | Application of Derivatives Exemplar PDF |
| Chapter 7 | Integrals Exemplar PDF |
| Chapter 8 | Application of Integrals Exemplar PDF |
| Chapter 10 | Vector Algebra Exemplar PDF |
| Chapter 11 | Three Dimensional Geometry Exemplar PDF |
| Chapter 12 | Linear Programming Exemplar PDF |
| Chapter 13 | Probability Exemplar PDF |
NCERT Exemplar Class 12 Maths Differential Equations: 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
| 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.
NCERT Exemplar Class 12 Maths Differential Equations - Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 12 Maths Differential Equations for free?
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