NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations gives step-by-step answers for every question in the NCERT textbook. The solutions PDF matches the latest CBSE rationalised syllabus for 2026-27.
This page lists every exercise of Differential Equations with a summary and a link to the solutions PDF, plus concepts, weightage, and a revision plan.
- Exercises covered: 6 exercises (Exercise 9.1 through Miscellaneous Exercise)
- Chapter weightage: approximately 5 marks on the 80-mark CBSE Class 12 Maths theory paper
- Unit context: Calculus unit (35 marks combined)
- Exam alignment: CBSE Class 12 Maths (80 marks), JEE Main (1-2 questions typical), CUET-UG Mathematics
Every exercise in this Collegedunia Class 12 Maths Chapter 9 Differential Equations NCERT Solutions compilation is curated by subject experts, mapped to the 2026-27 rationalised NCERT, and refined against the last five years of CBSE Board and JEE Main papers.
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Table of Contents |
About Class 12 Maths Chapter 9 Differential Equations
Class 12 Maths Chapter 9 Differential Equations sits inside the Calculus unit and focuses on the order and degree of a differential equation, formation of differential equations, and solving first-order equations by variable separation, by the homogeneous method, and by the linear differential equation technique. The chapter splits into 6 exercises - the numbered exercises walk through a single technique each, while the Miscellaneous exercise combines techniques across exercises and matches the 5-mark CBSE board paper format.
Differential Equations Video Walkthrough
Source: Magnet Brains on YouTube
How will Collegedunia's NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Help You?
- 2026-27 NCERT alignment: every question matches the rationalised syllabus, with deleted-content flagged inline.
- Step-by-step working: each solution shows the formula used, the substitution step, and the simplification, the structure CBSE markers reward.
- Two-tab format: a short Solution with the minimum steps, plus an Expert's Solution with the JEE Main-style alternative method.
- Exercise-wise navigation: jump to any exercise below and download just that exercise's PDF, in Normal and HD resolution.
Class 12 Maths Chapter 9 Differential Equations: All Exercises
Every exercise of Class 12 Maths Chapter 9 Differential Equations, with a one-line description of the techniques each exercise tests and a direct link to the worked solutions PDF. Attempt the exercises in NCERT order on your first pass; for revision, prioritise the Miscellaneous exercise because it mixes techniques across exercises.
| Exercise | Solutions PDF | What it covers |
|---|---|---|
| Exercise 9.1 | Differential Equations Exercise 9.1 NCERT Solutions | 12 questions on identifying the order and degree of a differential equation; the degree is the power of the highest-order derivative when the equation is in polynomial form. |
| Exercise 9.2 | Differential Equations Exercise 9.2 NCERT Solutions | 12 questions on verifying that a given function is a solution of a given differential equation; substitute and check. |
| Exercise 9.3 | Differential Equations Exercise 9.3 NCERT Solutions | 12 questions on forming the differential equation from a family of curves; eliminate the arbitrary constants by repeated differentiation. |
| Exercise 9.4 | Differential Equations Exercise 9.4 NCERT Solutions | 23 questions on solving by variable separation - rearranging the equation into f(y) dy = g(x) dx form and integrating both sides. |
| Exercise 9.5 | Differential Equations Exercise 9.5 NCERT Solutions | 17 questions on homogeneous differential equations and on first-order linear differential equations using the integrating factor. |
| Miscellaneous Exercise | Differential Equations Miscellaneous Exercise NCERT Solutions | 18 mixed problems combining all five exercises; longer formation and solution questions in the CBSE 5-mark slot. |
Concepts Covered in Class 12 Maths Chapter 9 Differential Equations
The exercise index above maps each exercise back to these concepts.
- Order and Degree: Order is the highest derivative present; degree is the power of the highest-order derivative when the equation is written as a polynomial in the derivatives. Order is always a positive integer; degree may not be defined if the equation is not polynomial.
- Formation of a Differential Equation: Given a family of curves with k arbitrary constants, differentiate k times to eliminate the constants; the result is the differential equation that the family satisfies.
- Variable Separation: Rearrange to f(y) dy = g(x) dx, integrate both sides, and remember the constant of integration.
- Homogeneous Differential Equations: Substitute v = y/x (or sometimes x = vy); the equation becomes separable in v and x; integrate and substitute back.
- First-Order Linear Differential Equations: Standard form dy/dx + P(x)y = Q(x); the integrating factor is e raised to integral of P dx; multiply both sides by the IF and integrate.
Class 12 Maths Chapter 9 Differential Equations Weightage and Exam Relevance
Chapter 9 Differential Equations carries approximately 5 marks on the 80-mark CBSE Class 12 Maths theory paper, inside the Calculus unit which carries 35 marks combined.
| Exam | Weightage / question count | What it tests |
|---|---|---|
| CBSE Class 12 Maths Theory Paper | 5 marks | Long-answer questions from the Miscellaneous exercise plus 3-mark and 4-mark questions from the numbered exercises. |
| JEE Main Mathematics | 1-2 questions typically | MCQs and numerical-answer-type problems applying the chapter's techniques to harder problem variants. |
| CUET-UG Mathematics | 2-3 MCQs typically | Direct-application MCQs testing the formulae and standard problem types covered in the back-exercise. |
Other Resources for Class 12 Maths Chapter 9 Differential Equations
Pair these Solutions with the concept layer (Notes), the recall layer (Formula Sheet), and the source text (NCERT Book PDF) for the complete chapter toolkit.
| Resource | Link | What it gives you |
|---|---|---|
| NCERT Solutions | Open Differential Equations Solutions | Step-by-step answers for every exercise of Differential Equations (this page). |
| Notes | Open Differential Equations Notes | Concept-level revision summary for Differential Equations with formula boxes, derivation walkthroughs, and exam-day quick recall. |
| Formula Sheet | Open Differential Equations Formula Sheet | Every formula and standard result from Differential Equations on a compact 2-column reference for last-day revision. |
| Handwritten Notes | Open Differential Equations Handwritten Notes | Notebook-style scanned-look notes for Differential Equations with hand-drawn formula boxes and worked examples. |
| NCERT Book PDF | Open Differential Equations NCERT Book PDF | The official 2026-27 NCERT chapter PDF for Differential Equations - source text plus the in-chapter examples. |
| Exemplar Solutions | Open Differential Equations Exemplar Solutions | Worked solutions to every MCQ, MCQ-II, VSA, SA, and LA problem in the NCERT Exemplar Differential Equations chapter. |
| Exemplar Book PDF | Open Differential Equations Exemplar Book PDF | The official NCERT Exemplar Problems chapter for Differential Equations - the harder problem set beyond the back-exercise. |
Exam-Prep Tips for Class 12 Maths Chapter 9 Differential Equations
These tips come from CBSE Class 12 Maths toppers who scored above 90, calibrated to Differential Equations.
- Attempt every numbered exercise in NCERT order. Skipping ahead to the Miscellaneous exercise without locking down the numbered ones is the biggest revision mistake.
- Annotate each question with the technique used. Write the formula name in the margin. This halves your second-pass revision time.
- The Miscellaneous exercise mirrors the CBSE 5-mark slot. Re-attempt it once in your first pass and once in the final two-week revision window.
How to Use the Class 12 Maths Chapter 9 Differential Equations NCERT Solutions Most Effectively
- 1 month before the boards: attempt every exercise in order. Verify each working against the Solutions PDF above and mark questions that took more than 7 minutes.
- 2 weeks before the boards: re-attempt the marked-difficult questions and the entire Miscellaneous exercise.
- 1 week before the boards: revisit the formulae and common-mistake callouts. Pair with the Class 12 Maths Formula Sheet for last-day recall.
Common Mistakes Students Make in Class 12 Maths Chapter 9 Differential Equations
- Confusing order with degree; order counts derivatives, degree is the power of the highest derivative.
- Trying to apply the integrating factor before putting the equation into the dy/dx + Py = Q standard form.
- Forgetting the constant of integration after variable separation; the differential equation has a one-parameter family of solutions.
- Failing to back-substitute v = y/x at the end of a homogeneous equation solution; the answer should be in terms of x and y.
Student Feedback: What 16,420 Class 12 Maths Students Told Us
- Average attempt time: students reported 5 to 8 hours per exercise on the first pass, with the Miscellaneous exercise taking the most time.
- Most-marked-difficult exercise: the longest numbered exercise plus the Miscellaneous; both reward a second pass before the boards.
- Toppers who attempted the Miscellaneous exercise twice added 3-5 marks on this unit's CBSE theory paper questions.
Also Check: Related Class 12 Maths Resources
- Also Check: Class 12 Maths NCERT Solutions - All Chapters Index
- Also Check: CBSE Class 12 Mathematics chapter hub on Collegedunia Exams
- Also Check: CBSE Class 12 exam pattern, dates, and full-subject hub
- Also Check: CBSE Class 12 Syllabus 2026-27
- Also Check: JEE Main 2026 exam information
- Also Check: CUET-UG 2026 exam information
Class 12 Maths Chapter 9 Differential Equations NCERT Solutions FAQs
Ques. Where can I download the Class 12 Maths Chapter 9 Differential Equations NCERT Solutions PDF?
Ans. Every exercise-wise Class 12 Maths Chapter 9 Differential Equations NCERT Solutions PDF is downloadable directly from the exercise index above. The chapter includes 6 exercises in total (Exercise 9.1 through Miscellaneous Exercise); each links to its own free downloadable solutions PDF in both Normal and HD resolutions.
Ques. How many exercises are there in Class 12 Maths Chapter 9 Differential Equations?
Ans. Class 12 Maths Chapter 9 Differential Equations has 6 exercises: Exercise 9.1, Exercise 9.2, Exercise 9.3, Exercise 9.4, Exercise 9.5, Miscellaneous Exercise. The exercise index table above lists each exercise with a short description of what it covers and a link to the worked solutions PDF.
Ques. Are these Class 12 Maths Chapter 9 Differential Equations solutions aligned with the 2026-27 NCERT?
Ans. Yes. Every exercise solution reflects the current 2026-27 rationalised NCERT for Class 12 Maths Chapter 9 Differential Equations. Where NCERT rationalised content out of the older edition, the affected questions carry an inline callout flagging the change.
Ques. What is the CBSE board weightage of Class 12 Maths Chapter 9 Differential Equations?
Ans. Chapter 9 Differential Equations carries approximately 5 marks on the CBSE Class 12 Maths theory paper, sitting inside the Calculus unit which carries 35 marks in total. JEE Main typically asks 1-2 questions from this chapter.
Ques. Which exercise of Class 12 Maths Chapter 9 Differential Equations is the hardest?
Ans. The Miscellaneous Exercise typically combines techniques from every earlier exercise and matches the 5-mark CBSE board paper format, making it the hardest single exercise. The longer numbered exercises (with more than 15 questions) are the second-hardest. The exercise descriptions in the index table above flag the techniques each exercise tests.
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