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NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations Exercise 9.3

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Chapter 9 – Differential Equations Exercise 9.3

1.

Q1 Class 12 differential equation with variable separable form

Class-12 Differential Equations Exercise-9.3 Question 1 separated variables and integrated form - NCERT Answer

2.

Exercise 9.3 Q2 – equation involving substitution method

Q2 – transformed equation using substitution

3.

Q3 differential equation featuring trigonometric terms

Q3 differential equation solution using trigonometric identity

4.

Q4 NCERT – equation requiring integration technique

Q4 integration approach to solve linear DE

Q4 simplification and rearrangement step

5.

Class 12 Q5 – exact form differential equation setup

Q5 exact equation identified and solved initially

6.

equation involving exponential and constant terms

Q6 exponential and variable terms integrated

7.

Differential equation with quadratic function – Q7

Q7 transformation and variable isolation

8.

Exercise 9.3 Q8 – linear form with variable coefficients

9.

Q9 NCERT – differential equation with initial value

Q9 separated form and integration initiation

Q9 integration carried out and simplified

10.

Q10 involving logarithmic terms in integration

Class-12 Differential Equations Exercise-9.3 Question 11-14 -NCERT

11.

Q11 Class 12 – Bernoulli’s equation transformation

Q11 integration after converting to linear

12.

Q12 substitution-based differential equation

Class-12 Differential Equations Exercise-9.3 Question 12 integration with rational expression
- NCERT Answer

Class-12 Differential Equations Exercise-9.3 Question 12 simplification and steps outlined- NCERT Answer

13.

Q13 featuring rational function with derivatives

Class-12 Differential Equations Exercise-9.3 Question 13 rational differential equation solution
- NCERT Answer

14.

Class-12 Differential Equations Exercise-9.3 Question 14 -trigonometric integration in differential equation-NCERT

Class-12 Differential Equations Exercise-9.3 Question 14 trigonometric substitution applied- NCERT Answer

15.

Class-12 Differential Equations Exercise-9.3 Question 15-omplex exponential equation-NCERT

Class-12 Differential Equations Exercise-9.3 Question 15 exponential DE transformation
- NCERT Answer

Class-12 Differential Equations Exercise-9.3 Question 15 integration and simplification step- NCERT Answer

16.

Class-12 Differential Equations Exercise-9.3 Question 16 -integrable expression with constants-NCERT

Class-12 Differential Equations Exercise-9.3 Question 16 separated equation and integration applied
- NCERT Answer

Class-12 Differential Equations Exercise-9.3 Question 16 solved step-by-step- NCERT Answer

17.

Class-12 Differential Equations Exercise-9.3 Question 17-product rule-based differential-NCERT

Class-12 Differential Equations Exercise-9.3 Question 17 product rule-based equation simplified
- NCERT Answer

18.

Class-12 Differential Equations Exercise-9.3 Question 18 -involving multiple integration steps-NCERT

Class-12 Differential Equations Exercise-9.3 Question 18 equation simplified using logarithmic property- NCERT Answer

Class-12 Differential Equations Exercise-9.3 Question 18 integration completed
- NCERT Answer

19.

Class-12 Differential Equations Exercise-9.3 Question 19 -separable form with substitution-NCERT

Class-12 Differential Equations Exercise-9.3 Question 19 solution mid-step with variables
- NCERT Answer

Class-12 Differential Equations Exercise-9.3 Question 19 expression with constant- NCERT Answer

20.

Class-12 Differential Equations Exercise-9.3 Question 20-linear equation solved by IF method
-NCERT

Class-12 Differential Equations Exercise-9.3 Question 20 linear DE approach with IF- NCERT Answer

21.

Class-12 Differential Equations Exercise-9.3 Question 21-exponential function in DE application-NCERT

Class-12 Differential Equations Exercise-9.3 Question 21 solution involving exponentials- NCERT Answer

Class-12 Differential Equations Exercise-9.3 Question 21 detailed steps to isolate variable- NCERT Answer

22.

Class-12 Differential Equations Exercise-9.3 Question 22-inverse trigonometric terms in DE-NCERT

Class-12 Differential Equations Exercise-9.3 Question 22 inverse trigonometric integration- NCERT Answer

23.

Class-12 Differential Equations Exercise-9.3 Question 23-integration-heavy differential equation-NCERT

Class-12 Differential Equations Exercise-9.3 Question 23 NCERT multi-step integration- NCERT Answer

Download Exercise 9.3 NCERT Solutions PDF

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Download Chapter 9 – Differential Equations NCERT Solutions PDF

Class 12 Maths Chapter 9 – Differential Equations: All Exercises

Exercise	Link
Exercise 9.1	View Solutions
Exercise 9.2	View Solutions
Exercise 9.4	View Solutions
Exercise 9.5	View Solutions

Class 12 Differential Equations- Exercise 9.3 Overview

One strong technique utilized in mathematical modelling and real-life situations is the integration by factors (I.F.) method, which students learn about in Exercise 9.3. This approach solves first-order linear differential equations. From determining the standard form to implementing integration principles with clarity, this approach opens the way to more methodically structured problem-solving whereby every step follows a logical procedure.

Students will practice transforming differential equations into the linear form dy/dx + Py = Q and subsequently using the I.F. approach to identify the answer in this activity. This sharpens your algebra and calculus coordination as well as develops your knowledge of the several approaches to differential equations.

Walking through each question with thorough steps in our Differential Equations Class 12 NCERT Solutions Exercise 9.3 helps simplify the I.F. technique. Whether it’s figuring the integrating factor, reorganizing terminology, or streamlining the answer, our solutions are meant to help students at all levels.

Matching the 2025 NCERT Maths syllabus, mastery of this activity is essential for Class 12 boards and competitive tests. It gives you confidence in managing abstract mathematical concepts and prepares you with necessary tools to solve dynamic systems in disciplines such physics, economics, and engineering.

FAQs – Differential Equations Class 12 Exercise 9.3 NCERT

How do I identify if an equation is linear in form?

If the equation can be written as dy/dx + Py = Q, where P and Q are functions of x (or constants), it’s in linear form and suitable for this method.

How do you figure out the Integrating Factor (I.F.)?

Applied to both sides of the equation, the I.F. e^(∫P dx) makes the left-hand side integrable as a product rule derivative.

Why would this approach help one address issues from daily life?

This method is rather useful in modelling growth and decay, electrical circuits, and rate-based systems in economics and biology as well as in modelling development and decay in mathematics and physics.

Does the solution benefit from constant of integration?

Indeed, it reflects the family of solutions unless the problem states initial or boundary requirements.

Where are solved Exercise 9.3 examples available?

We have thoroughly described Differential Equations Class 12 NCERT Solutions Exercise 9.3 on Cogniks.com to enable students to solve clearly and confidently.