NCERT Solution Class 12 Chapter 9- Differential Equations

NCERT Solutions For Class 12 Maths Chapter 9 PDF Free Download

The NCERT Solutions for Class 12 maths Chapter 9, Differential Equations, is available here. In this chapter, students learn about order and degree of differential equations, method of solving a differential equation, their properties and much more. This topic is extremely important for scoring high in both CBSE board exams and competitive exams.

The concepts of Differential Equations are given in this chapter in a detailed and easy to understand manner. These class 12 NCERT solutions for Differential Equations are very simple and can help the students in understanding the problem solving method very easily. Students can reach for these NCERT solutions and download it for free to practice them offline as well. These solved questions make the students understand the method of applying the concepts of Differential Equations in each problem.

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NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations

The major concepts of Maths covered in Chapter 9- Differential Equations of NCERT Solutions for Class 12 includes:

9.1 Introduction

9.2 Basic Concepts

9.2.1 Order of a differential equation

9.2.2 Degree of a differential equation

9.3 General and Particular Solutions of a Differential Equation

9.4 Formation of a Differential Equation whose General Solution is given

9.4.1 Procedure to form a differential equation that will represent a given family of curves

9.5 Methods of Solving First Order, First Degree Differential Equations

9.5.1 Differential equations with variables separable

9.5.2 Homogeneous differential equations

9.5.3 Linear differential equations

Exercise 9.1 Solutions 12 Questions

Exercise 9.2 Solutions 12 Questions

Exercise 9.3 Solutions 12 Questions

Exercise 9.4 Solutions 23 Questions

Exercise 9.5 Solutions 17 Questions

Exercise 9.6 Solutions 19 Questions

Miscellaneous Exercise On Chapter 9 Solutions 18 Questions

NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations

The chapter Differential Equations belongs to the unit Calculus, that adds up to 35 marks of the total marks. There are 6 exercises along with a miscellaneous exercise in this chapter to help students understand the concepts of Differential Equations clearly. The Chapter 9 of NCERT Solutions for Class 12 Maths discusses the following:

  1. An equation involving derivatives of the dependent variable with respect to independent variable (variables) is known as a differential equation.
  2. Order of a differential equation is the order of the highest order derivative occurring in the differential equation.
  3. Degree of a differential equation is defined if it is a polynomial equation in its derivatives.
  4. Degree (when defined) of a differential equation is the highest power (positive integer only) of the highest order derivative in it.
  5. A function which satisfies the given differential equation is called its solution. The solution which contains as many arbitrary constants as the order of the differential equation is called a general solution and the solution free from arbitrary constants is called a particular solution.
  6. To form a differential equation from a given function we differentiate the function successively as many times as the number of arbitrary constants in the given function and then eliminate the arbitrary constants.
  7. Variable separable method is used to solve such an equation in which variables can be separated completely i.e. terms containing y should remain with dy and terms containing x should remain with dx.

Key Features of NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations

Learning the chapter Differential Equations enables the students to understand the following:

Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by the method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:

Key Features of NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations

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