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NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations

Instasolv’s expert Maths teachers draft the NCERT Solutions for Class 12 Maths Chapter 9-Differential Equation on the basis of the latest CBSE Class 12 Maths Syllabus. Our NCERT Solutions cover all important topics from this chapter. Some of the significant topics covered here include the meaning of a differential equation, order and degree of a differential equation, the formation of a differential equation, and solutions of differential equations.

This chapter also teaches you to solve differential equations of the first order and first degree with the help of various methods such as Inspection Method, Variable Separable Method, Linear Differential Equation, Exact Differential Equation, Differential Equation Reducible to Linear Form, Clairaut Form for Differential equation, Orthogonal trajectory, Differential Equation Reducible to Variables Separable Method, Homogeneous Differential Equation and Differential Equations Reducible to Homogeneous Equation. There are 6 exercises and 1 miscellaneous exercise at the end of the chapter. Our NCERT Solutions answer all questions from all exercises in a step by step manner to help you quickly become thorough with the concepts of the chapter.

Our NCERT Solutions have been drafted in a manner to help make the learning process more fun. Interesting, stimulating and effective. They ensure that your concepts are clear and strong. They are perfect for learning and revising during your board exams to score high marks.

NCERT Class 12 Maths Chapter 9

NCERT Solutions for Class 12 Maths Chapter 9-Differential Equation comprises some of the most important concepts of the differential equation and detailed explanation along with solved examples. Some of the topics covered have been discussed below.

Differential equation

This section of CBSE NCERT Class 12 Maths Chapter 9 covers the meaning of a differential equation, order and degree of a differential equation, linear and nonlinear differential equations, and the formation of differential equations.

Solutions of a Differential Equation

This section of the chapter tells you that when the relations between the variables not involving the differential coefficients in a manner such that the derivative or relation obtained from it satisfies the given equation is termed as a solution of a differential equation. 

Here you will learn about the general solution of a differential equation and the particular solution of a differential equation. 

Solutions of Differential Equations of the First Order and First Degree

This section of NCERT CBSE Class 12 Maths Chapter 9 teaches you that a differential equation of the first order and first degree can be solved by the various methods. Some of them are as follows.

 

  • Variable Separable Method

 

It can be said that the variable has been separated when the equation can be reduced to the form of f(x) dx + g(y) dy = 0. When this reduced form is integrated, we get,

 ∫ f(x) dx + ∫ g(y) dy = C, = C, where C is any arbitrary constant.

 

  • Exact Differential Equation

 

In this part of the chapter, you will learn that,

Differential equation P(x,y) dy + Q(x,y) dy = 0 is termed as an exact differential equation.If a function u (x, y) exist such that, 

du = Pdx + Qdy.

 

  • Linear Differential Equation

 

Here you will learn that a linear differential equation of the first order can have any one of the forms given below

  1. dy / dx + Py = Q, where P and Q are functions of x or constants.
  2. dx/dy  + Rx = S, Where R and S are functions of y or constants.

Other methods taught in Class 12 Maths Differential Equation include Inspection Method, Differential Equation Reducible to Linear Form, Clairaut Form for Differential equation, Orthogonal trajectory, Differential Equation Reducible to Variables Separable Method, Homogeneous Differential Equation and Differential Equations Reducible to Homogeneous Equation.

NCERT CBSE Class 12 Maths Chapter 9 Exercises-Discussion

Our NCERT Solutions for Class 12 Maths Chapter 9-Differential Equation contain step by step solutions of all 6 exercises of the chapter. The exercises have been discussed below.

Exercise 9.1

Exercise 9.1 helps you to become familiar with the methods of solutions that are a function of differential equations. In this exercise, you will find a total of 11 questions. The questions of this exercise ask you to find the order and degree of given differential equations.

Exercise 9.2

In this exercise, you will find a total of 12 questions. The first 10 questions ask you to find out whether the given explicit or implicit functions are a solution of the corresponding differential equation. Questions 11 and 12 are MCQs.

Exercise 9.3

This exercise includes a total of 12 questions. The first 5 questions ask you to form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. The rest of the questions from this exercise also deal with the procedure of formation of differential equations that represent a given family of curves. Question 11 and 12 are MCQs.

Exercise 9.4

Under this exercise of NCERT CBSE Class 12 Maths Chapter 9, you will come across 23 questions. The first 10 questions of this chapter ask you to find out general solutions of the given differential equation. For questions 11 to 14, you will have to find a particular solution that will satisfy the given differential equation. In questions 15 to 23, you will have to solve differential equations that represent either a curve, two points joining a curve, or a circle, or group of circles. Some of the questions of this exercise are scenario-based questions such as questions 20, 21 and 22.

Exercise 9.5

This exercise consists of 17 questions.  The first 10 questions will help you learn the method of proving the homogeneity of a differential equation. For questions 11 to 15 you have to find the particular solution of the differential equations based on given conditions. Questions 16 and 17 are multiple-choice questions where you will have to solve the given differential equation and pick the correct alternative from given options. Both of these questions are related to the homogeneous differential equation.

Exercise 9.6

In this exercise, you will find 19 questions. For questions 1 to 12, you will have to find the general solution of given differential equations. For questions 13 to 15, you will have to find a particular solution satisfying the given condition.  Questions 16 and 17 are of the same type and questions 18 and 19 are of the same type.

This chapter also comprises a miscellaneous exercise comprising 18 questions that cover all the topics discussed in this chapter.

Benefits of NCERT Solutions for Class 12th Maths Chapter 9- Differential Equations

There are many advantages associated with preparing for your Class 12 Board Exams from our smart, systematic and comprehensive NCERT Solutions for Class 12th Maths Chapter 9- Differential Equations. Some of them have been cited below.

  1. Our effective study methodologies and Maths shortcuts help you learn quickly and score more marks in your Board exams. 
  2. Our NCERT Solutions cover all concepts in details and have been drafted as per the latest CBSE Syllabus.
  3. They cover a wide range of question types important from the board exam perspective. They give you ample practice to become absolutely thorough with all concepts of the chapter.
  4. They leave no scope for any conceptual doubts or questions.
  5. They have been specifically designed to improve your retention rate and help you make use of your full potential.
  6. They have been devised to make learning a faster and more effective process.