NCERT Solutions for Class 9 Political Science Chapter 2

August 8, 202239 Insightful Publications

**NCERT Solutions for Differential Equations Exercise 9.2 Class 12 Maths:** CBSE Class 12 Maths contains numerous important chapters and topics that are very important for students in the future. Many of these topics hold tremendous application value across various technical courses and industries. One of these important chapters in NCERT Class 12 Maths is Differential Equations. The NCERT Solutions for Differential Equations Exercise 9.2 Class 12 Maths in this article provides guidance to students on how to solve complex questions to prepare for the CBSE 12th board exams.

The solutions are provided for exercise 9.2 as per the latest NCERT Class 12 Maths textbook. We have given detailed step-wise solutions prepared by Embibe’s subject experts. These solutions will help students prepare for CBSE 12th exam questions and how to solve them. Read on for the NCERT Solutions for Differential Equations Exercise 9.2 Class 12 Maths.

The ninth chapter in NCERT Class 12 Maths is Differential Equations and it is grouped under the unit, Calculus. Differential Equations are equations that deal with unknown functions and their derivatives. These functions represent the physical quantities and the derivatives represent their rate of change. The relation between the two is represented by the Differential Equation.

Differential Equations are commonly used in various fields including Physics, Engineering, Economics and Biology. In NCERT 12th Maths Chapter 9 Differential Equations, students learn about the basic concepts of equations and functions, sets of functions, and their properties. The chapter teaches how these equations can be applied to various situations.

Some types of Differential Equations that are discussed in the chapter are:

- Ordinary Differential Equation
- Partial Differential Equation
- Linear Differential Equation
- Non-linear Differential Equation
- Homogeneous Differential Equation
- Non-homogeneous Differential Equation

The topics that are covered in NCERT Class 12 Chapter 9 maths are given below:

Section | Topics | Sub-Topics |

9.1 | Introduction | Order of a differential equation degree of a differential equation |

9.2 | Basic Concepts | – |

9.3 | General and Particular Solutions of a Differential Equation | – |

9.4 | Formation of a Differential Equation whose General Solution is given | 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 | Differential equations with variables separableHomogeneous differential equations linear differential equations |

Exercises given in the NCERT Maths textbook are very important for students to practice and understand. The CBSE 12th board exam questions are based on these exercises and in previous years, direct questions have been asked from these exercises.

Chapter 9 of Class 12 Maths contains 5 exercises in total containing questions based on the five sub-topics respectively. Embibe experts have provided the best detailed, step-wise solutions for students to refer to and practice. Students can download PDFs of the Differential Equations NCERT Solutions Exercise 9.2 Class 12 Maths from the link below for free.

**Download NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations**

Students can also download the NCERT Solutions for Class 12 Maths all chapters from Embibe.

To familiarise with how Differential Equations questions are to be approached and solved, we have provided a few Differential Equations sample questions with solutions that can be very helpful for students’ exam practice:

**Question 1:** ??/?? + cos? = 0.

**Solution:** ??/?? + cos? = 0

?′ + cos? = 0

Highest order of derivative =1

∴ Order = 1

Degree = Power of ?′

Degree = 1

**Question 2:** (??/??)^{2} + 3 (?^{2}?/??^{2}) = 4

**Solution:** (??/??)^{2} + 3 (?^{2}?/??^{2}) = 4

Highest order of derivative = 2

Order = 2

Degree = Power of ?

Degree = 1

**Practice 12th CBSE Exam Questions**

**Question 3:** The number of arbitrary constants in the general solution of a differential equation of fourth order is:

(A) 0 (B) 2 (C) 3 (D) 4

**Solution:** We know that the number of constants in the general solution of a differential equation of order n is equal to its order.

Therefore, the number of constants in the general equation of the fourth-order differential equation is four.

Hence, the correct answer is D.

Note: The number of constants in the general solution of a differential equation of order n is equal to zero.

As iterated, NCERT Solutions for Class 12 Maths are very important for students’ 12th exam practice. There are plenty of benefits that students can gain by studying them thoroughly and practicing them. We have listed a few of the benefits of NCERT Solutions for Class 12 Maths:

**They provide a good grasp of concepts:**NCERT solutions provide students with good practice for exams and can help them get a good grasp of the various concepts. Since Maths is an application-based subject, these solutions can help students retain formulas and concepts better during exams, and subsequently, help them solve questions better and more efficiently.**They help students to get familiar with exam question formats:**CBSE and other relevant boards design the 12th Maths exam questions directly around NCERT in-text questions. In fact, many questions in previous years’ question papers have been directly taken from the NCERT back of text exercises. The NCERT solutions offer students the ideal way to solve the questions with step-wise guidance.**They are very beneficial for competitive exams as well:**Most competitive exams base their question papers around the NCERT curriculum. Going through the NCERT Solutions for Class 12 Maths thoroughly and practicing them not only gives students an edge in their 12th board exams, but it helps them simultaneously prepare for competitive exams such as JEE, BITSAT, etc.

We have provided some of the frequently asked questions below:

**Q.1: Where can I download NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations?****Ans:** Students can download NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations from Embibe. The links for Chapter 9 Ex 9.2 Class 12 Maths has been provided in this article along with the link to download NCERT Solutions for all chapters of Class 12 Maths. All the solutions have been prepared by Embibe’s subject experts with detailed explanations and step-wise solutions.

**Q.2: When is the CBSE Class 12 Maths board exam?****Ans:** The CBSE Class 12 Maths board exam is scheduled for June 7, 2022. The timing for the Maths paper is 10:30 am to 12:30 pm.

**Q.3: What are the topics covered in NCERT 12th Maths Differential Equations?****Ans:** The topics covered in NCERT 12th Maths Differential Equations are Introduction (to Differential Equations), Basic Concepts of Differential Equations, General and Particular Solutions of a Differential Equation, Formation of a Differential Equation whose General Solution is given, and Methods of Solving First Order, First Degree Differential Equations. The sub-topics have also been provided in this article.

**Q.4: What are Differential Equations?****Ans:** Differential Equations are equations that deal with unknown functions and their derivatives. These functions represent the physical quantities and the derivatives represent their rate of change. The relation between the two is represented by the Differential Equation.

**Q.5: What are General and Particular Solutions of a Differential Equation?****Ans:** The solutions which contain arbitrary constants are called general solutions of the differential equation. And, solutions free from arbitrary constants obtained from general solutions by giving particular values to the arbitrary constants are called particular solutions of the differential equation.

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