Table of Contents
The Miscellaneous Exercise in the NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations includes questions that cover all the topics in the chapter. This exercise is based on the following topics:
- 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
- Methods of Solving First Order, First Degree Differential Equations
NCERT Solutions for Class 12 Maths Ch-9 Differential Equations Miscellaneous Exercise – CBSE Free PDF Download
Access NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Miscellaneous Exercise
1. For each of the differential equations given below, indicate its order and degree (if defined)
(i) (d2y/dx2) + 5x(dy/dx)2 – 6y = log x
(ii) (dy/dx)3 – 4 (dy/dx)2 + 7y = sin x
(iii) (d4y/dx4) – sin (d3y/dx3) = 0
Solution:
(i) (d2y/dx2) + 5x(dy/dx)2 – 6y = log x
Rearranging the given equation, we get
(d2y/dx2) + 5x(dy/dx)2 – 6y – log x = 0
Hence, the highest order derivative present in the given differential equation is d2y/dx2.
Therefore, the order is 2.
Also, the highest power raised to d2y/dx2 is 1.
Hence, the degree is 1.
(ii) (dy/dx)3 – 4 (dy/dx)2 + 7y = sin x
Rearranging the given equation, we get
(dy/dx)3 – 4 (dy/dx)2 + 7y – sin x = 0
Hence, the highest order derivative present in the given differential equation is dy/dx.
Therefore, the order is 1.
And the highest power raised to dy/dx is 3.
Hence, the degree is 3.
Also Read: NCERT Solutions for Class 12 Maths
(iii) (d4y/dx4) – sin (d3y/dx3) = 0
The highest order derivative present in the given differential equation is d4y/dx4. Hence, the order is 4.
Since the given differential equation is not a polynomial equation, the degree of the equation is not defined.
2. Form the differential equation representing the family of curves given by (x- a)2 + 2y2 = a2, where a is an arbitrary constant.
Solution:
Given equation: (x- a)2 + 2y2 = a2
The given equation can be written as:
⇒ x2 + a2 – 2ax + 2y2 = a2
On rearranging the above equation, we get
⇒ 2y2 = 2ax – x2 …(1)
Now, differentiate equation (1) with respect to x,
⇒ 2 . 2y (dy/dx) = 2a – 2x
⇒ 2y(dy/dx) = (2a – 2x) /2
⇒ dy/dx = (a-x)/2y
⇒ dy/dx = (2ax – 2x2) / 4xy … (2)
From equation (1), we get
2ax = 2y2 + x2
Substitute the value in equation (2), and we get
dy/dx = [2y2 + x2 – 2x2]/4xy
dy/dx = (2y2 – x2) / 4xy
Therefore, the differential equation representing the family of curves given by (x- a)2 + 2y2 = a2 is (2y2 – x2) / 4xy.
Also Read: NCERT Solutions for Class 12
Frequently Asked Questions (FAQs)
Is Chapter 9 of Class 12 Maths difficult?
Math becomes easier for each student with practice. Maths will be simple for that kid after he or she has a firm grasp of the fundamental principles and has learned the techniques to solve each question. As a result, it's critical to master the fundamentals and practice thoroughly for all types of queries. In terms of complexity, the Class 12 Maths syllabus contains a combination of questions. The solutions may be found on the NCERT Solutions Class 12 Maths Chapter 9 website.
Are there answers to all of the textbook problems in the NCERT Solutions for Class 12 Maths Chapter 9?
The NCERT Solutions for Class 12 Maths Chapter 9 are created by subject specialists and are accessible in PDF format. These solutions are based entirely on the most recent CBSE Syllabus 2024-25, and they cover all of the key ideas for the second-term exam. The textbook questions are addressed in a step-by-step fashion based on the weighting of the marks in the second-term exams. Infinity learns has chapter-by-chapter and exercise-by-exercise PDF links that students can use to get their questions answered quickly.
What is the finest NCERT Class 12 Maths Chapter 9 Solution book?
By going to the Infinity Learn website and looking for Class 12 Maths solutions, you may get NCERT Class 12 Maths Solutions. Aside from that, you'll get access to a number of courses that will help you get good grades on math exams. The solutions to the exercises may be found on the NCERT Solutions Class 12 Maths Chapter 9 page. To download a PDF of the solutions, click on it.
