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NCERT Solutions Class 12 Maths Chapter 9 Differential Equations
NCERT Solutions for class 12 maths chapter 9 differential equations utilize the concepts of calculus to introduce a new topic called differential equations. Previously children were taught how to differentiate a given function f with respect to an independent variable, i.e., how to find f ′(x) for a given function f at each x in its domain of definition. Further how to find a function f whose derivative is the function g was also taught to students. Using these concepts a formal definition for differential equations can be given as an equation involving the derivative of the dependent variable with respect to the independent variable. We can also categorize these equations. A differential equation involving derivatives of the dependent variable with respect to only one independent variable is called an ordinary differential equation while partial differential equations are differential equations that involve derivatives with respect to more than one independent variable. NCERT solutions class 12 maths chapter 9 explains these topics in depth with exemplar problems.
Class 12 maths NCERT solutions chapter 9 shows another aspect of calculus. Once children are well-versed with the different methods of differentiating and integrating a function they can smoothly transition to solving the problems in this lesson. NCERT Solutions Chapter 9 differential equations have applications in finding the population growth and decay, determining the glucose absorption by the body, gauging the spread of epidemics as well as in solving various geometric questions involving different types of curves, download the exercises provided in the links below.
- NCERT Solutions Class 12 Maths Chapter 9 Ex 9.1
- NCERT Solutions Class 12 Maths Chapter 9 Ex 9.2
- NCERT Solutions Class 12 Maths Chapter 9 Ex 9.3
- NCERT Solutions Class 12 Maths Chapter 9 Ex 9.4
- NCERT Solutions Class 12 Maths Chapter 9 Ex 9.5
- NCERT Solutions Class 12 Maths Chapter 9 Ex 9.6
- NCERT Solutions Class 12 Maths Chapter 9 Miscellaneous Ex
NCERT Solutions for Class 12 Maths Chapter 9 PDF
November 11, 1675, is when the concept of differential equations was born because of Gottfried Wilhelm Freiherr Leibnitz (1646 - 1716) who gave a calculus identity. Leibnitz was actually interested in the problem of finding a curve whose tangents were prescribed. This led him to discover many associated concepts of differential equations. With several researchers working on the complexity of this topic the equations took a form as we see them today. The NCERT solutions class 12 maths has many such facts as well as tips to help kids combat monotony and study with enthusiasm. Given below are the links to all the exercise solutions.
☛ Download Class 12 Maths NCERT Solutions Chapter 9 Differential Equations
NCERT Class 12 Maths Chapter 9
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations
NCERT Solutions Class 12 Maths Chapter 9 differential equations is a difficult and long lesson. Thus, the only way to master the chapter is by regularly revising the topics. If kids have a strong foundation of the fundamentals it will be easier for them to go through the chapter and develop clear concepts. Given below is a detailed analysis of all the exercise questions to help students in their quest to get a good quality of education.
- Class 12 Maths Chapter 9 Ex 9.1 - 12 Questions
- Class 12 Maths Chapter 9 Ex 9.2 - 12 Questions
- Class 12 Maths Chapter 9 Ex 9.3 - 12 Questions
- Class 12 Maths Chapter 9 Ex 9.4 - 23 Questions
- Class 12 Maths Chapter 9 Ex 9.5 - 17 Questions
- Class 12 Maths Chapter 9 Ex 9.6 - 19 Questions
- Class 12 Maths Chapter 9 Miscellaneous Ex - 18 Questions
Topics Covered: Determining the order and degree of an equation, verifying the solution of a differential equation, and forming such an equation from the general solution, and how to solve a homogeneous and linear differential equation are the topics covered under the Class 12 Math NCERT Solutions.
Total Questions: There are 113 sums in Class 12 maths chapter 9 differential equations of a wide-ranging variety. 72 are tough problems that require students to use their mathematical acumen, 15 are simple and 26 are of a medium level.
List of Formulas in NCERT Solutions Class 12 Maths Chapter 9
NCERT solutions class 12 maths chapter 9 uses the formulas that have been listed in previous lessons on calculus to solve the differential equations. This chapter mainly focuses on the procedures to formulate a differential equation and solve them given certain conditions. Hence, revision of the calculus concepts taught earlier is very important in order to effectively combine both lessons. The NCERT solutions for class 12 maths chapter 9 have certain terminologies that kids need to be familiar with, a few of which are given below:
- General form of a differential equation: dy/dx = g(x), where y = f(x).
- General form of nth order derivative: dny/dxn.
- General form of a linear differential equation: dy/dx + Py = Q
FAQs on NCERT Solutions for Class 12 Maths Chapter 9
Why are NCERT Solutions Class 12 Maths Chapter 9 Important?
NCERT Solutions Class 12 Maths Chapter 9 form the basis of the board exams. The papers set by CBSE follow the pattern in the NCERT textbook. Additionally, these problems are curated in a way so as to give its readers a 360-degree view of the chapter. Thus, kids must use these to get a good grasp of the lesson as well as cross-check their answers after solving a question.
Do I Need to Practice all Questions Provided in NCERT Solutions Class 12 Maths Differential Equations?
Practice is the key to perfection. Thus, all the sums provided in the NCERT Solutions Class 12 Maths Differential Equations need to be practiced at least twice. This chapter introduces various new concepts that are built on previously learned topics and hence, can get confusing at times. By solving each problem students not only pave the way to securing a higher score in exams but also ensure that these topics can be fruitfully used in real-life applications.
What are the Important Topics Covered in Class 12 Maths NCERT Solutions Chapter 9?
All the topics in the NCERT Solutions Class 12 Maths Chapter 9 are equally important as they highlight a different aspect of differential equations. In addition to this, each section is also interlinked. Thus, to prevent any superficial knowledge as well as gaps in learning it is crucial for young minds to give an equal and ample amount of time to all parts of this chapter. It is also recommended to go through the previous subject matter that sees use in this lesson.
How Many Questions are there in NCERT Solutions Class 12 Maths Chapter 9 Differential Equations?
There are a total of 113 questions in the NCERT Solutions Class 12 Maths Chapter 9 Differential Equations that are divided among 7 exercises. Out of this, there is a miscellaneous exercise consisting of higher-order problems that require kids to think out of the box and apply their auxiliary mathematical skills in addition to repetitive revision. These are fantastic sums that help students get a holistic understanding of this topic.
How CBSE Students can utilize NCERT Solutions Class 12 Maths Chapter 9 effectively?
To effectively utilize the NCERT Solutions Class 12 Maths Chapter 9 the first step is to have a strong foundation of all the integration and differentiation formulas outlined in previous chapters. The next step is to create a link between these concepts and differential equations. Finally, students can apply these topics to various levels of questions and use the solutions to check if their answers, as well as steps, are correct.
Why Should I Practice Class 12 Maths NCERT Solutions Differential Equations Chapter 9?
By regularly practicing the NCERT Solutions Class 12 Maths Differential Equations Chapter 9 students will be able to build their confidence in solving questions on this topic. During any examination, be it boards or competitive, they will be able to attempt the paper stress-free leading to imminent success. Apart from this, by revising these solutions kids can ensure the formation of a strong mathematical foundation that will even help them in their careers.