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NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations - PDF Download

JEE Mains & Advanced

NCERT Solutions for class 12 maths Chapter 9 which is dedicated to "Differential Equations," is one of the most important chapters. Solving differential equations helps understand the behavior of dynamic systems. Many examples and exercises with solutions are included in Chapter 9 of the math textbook for class 12 in different sections and topics. The subject matter experts provided step-wise solutions for every question covered in this chapter. To master this chapter, students can rely on the comprehensive NCERT Solutions provided by eSaral. 

The most accurate explanations for each question in the chapter are included in the NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations. This chapter covers a wide range of topics, including the order and degree of differential equations, how to solve them, their properties, and much more in this chapter. Students can get a solid understanding of the concepts of differential equations by using the NCERT Solutions for Class 12 Maths to solve the questions in the various exercises. These NCERT Solutions for Class 12 Maths Chapter 9 are available for free to download so that students can practice them anytime.

NCERT Solutions for Class 12 Maths Chapter 9 - Differential Equations I Free PDF

In NCERT Solutions for class 12 maths chapter 9 we use formulas to solve the Differential Equations. This chapter primarily focuses on how to formulate and solve differential equations under particular conditions. You will find it simpler to understand the chapter and form precise concepts if you have a solid foundation in the fundamentals. Our well-explained solutions can help you understand concepts and assist you to achieve high scores in exams. Our expert teachers at eSaral have designed the NCERT Solutions for chapter 9 in an easy-to-understand format. The NCERT Solutions pdf for class 12 maths chapter 9 is available on eSral. 

Important Topics Covered in Chapter 9 - Differential Equation

9.1 Introduction - You will be reminded of what you learned about differentiation in the last chapter. You would remember how changing an independent variable helped  to differentiate between two functions, f. 

Here, you will learn some basic concepts of differential equations, General and Particular solutions of a differential equation and some techniques to solve first order, first degree differential equations.

9.2 Basic Concepts

  1. Order of a Differential Equation
  2. Degree of a Differential Equation

In this section, The fundamentals of the differential equation and its prevalent representation will be covered. You will find that a differential equation is one that, in addition to the dependent and independent variables, also contains derivatives of the dependent variable with respect to the independent variable. 

You would be aware of the concept of the order of differential equations, which is the highest derivative of a dependent variable present in the equation. You would be familiar with the degree of differential equation, which is only possible when the differential equation is polynomial. The degree of the differential equation is determined by the higher of the highest order derivatives of the differential equation.

9.3 General and Particular Solutions of a Differential Equation - In this section, you will be presented with the distinctions between general and specific differential equation solutions. A solution to a differential equation that is a general solution is one in which the independent arbitrary constant of the equation is equal to the sequence of the equation.

9.4 Methods of Solving first order, first degree Differential Equation

  1. Differential Equations with variables separable
  2. Homogeneous Differential Equations
  3. Linear Differential Equations

This section will teach you three different ways to solve a first-order and first-degree differential equation.

 NCERT Solutions for Class 12 Maths Chapter 9 Exercises

At the end of every chapter, There are well-organized exercises to help students learn. These exercises are meant to challenge students and help them understand what's been said in the chapter. 

So, let's take a look at some of the NCERT solutions for class 12 maths chapter 9 exercises.

Exercise 9.1

12 Questions & Solutions

Exercise 9.2

12 Questions & Solutions

Exercise 9.3

23 Questions & Solutions

Exercise 9.4

17 Questions & Solutions

Exercise 9.5

19 Questions & Solutions

Miscellaneous Exercise

15 Questions & Solutions

Benefits of Downloading the Class 12 Maths NCERT Solutions Chapter 9 -  Differential Equations

The NCERT Solutions to Chapter 9-Differential Equations provide a range of benefits that can help to improve their comprehension and performance. Here, We will outline some of the primary benefits of downloading and using these solutions.

  1. The NCERT solutions of class 12 chapter 9 are presented in a straightforward manner, allowing students to comprehend the concepts and methods associated with the solution of differential equations.
  2. The differential equations in class 12th maths cover all the topics covered in the chapter of Class 12 Maths, thus ensuring that students are adequately prepared for their examinations.
  3. The objective of differential equation class 12 solutions is to enhance the conceptual clarity of the students, rather than to provide them with final solutions. This contributes to the development of a solid basis in the topic.
  4. With the help of NCERT Solutions, the students can cross-check their answers and spot any errors they may have made. This fault-free learning process improves the students’ problem-solving abilities and confidence.
  5. Time management is really important when it comes to Class 12 board exams. NCERT Solutions for class 12 maths chapter 9 is a great resource that can help students figure out the best and most efficient ways to solve differential equations problems.

Frequently Asked Question

Question 1. What is a Differential Equation?
Answer 1. A differential equation is an equation that involves the derivative of a dependent variable with respect to an independent variable (varieties). It is an important topic for students of class 12 maths. Use our NCERT Solutions to solve questions in chapter 9. 

Question 2. What are the most important topics covered in Chapter 9 of Class 12 NCERT Solutions?

Answer 2. All the topics in NCERT solutions class 12 math chapters 9 are just as important because they focus on different aspects of differential equations. Here are some important topics of chapter 9 Differential Equations.

  • Basic Concepts

      1.Order of a Differential Equation

      2.Degree of a Differential Equation

  • General and Particular Solutions of a Differential Equation 

  • Methods of Solving first order, first degree Differential Equations

     1.Differential Equations with variables separable

     2.Homogeneous Differential Equations

     3.Linear Differential Equations


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