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) (d ^{2}y/dx^{2}) + 5x(dy/dx)^{2} – 6y = log x**

**(ii) (dy/dx) ^{3} – 4 (dy/dx)^{2} + 7y = sin x**

**(iii) (d ^{4}y/dx^{4}) – sin (d^{3}y/dx^{3}) = 0**

**Solution:**

**(i) (d ^{2}y/dx^{2}) + 5x(dy/dx)^{2} – 6y = log x**

Rearranging the given equation, we get

(d^{2}y/dx^{2}) + 5x(dy/dx)^{2} – 6y – log x = 0

Hence, the highest order derivative present in the given differential equation is d^{2}y/dx^{2}.

Therefore, the order is 2.

Also, the highest power raised to d^{2}y/dx^{2} 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) (d ^{4}y/dx^{4}) – sin (d^{3}y/dx^{3}) = 0**

The highest order derivative present in the given differential equation is d^{4}y/dx^{4}. 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} + 2y^{2} = a^{2}, where a is an arbitrary constant.**

**Solution:**

Given equation: (x- a)^{2} + 2y^{2} = a^{2}

The given equation can be written as:

⇒ x^{2} + a^{2} – 2ax + 2y^{2} = a^{2}

On rearranging the above equation, we get

⇒ 2y^{2} = 2ax – x^{2} …(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 – 2x^{2}) / 4xy … (2)

From equation (1), we get

2ax = 2y^{2} + x^{2}

Substitute the value in equation (2), and we get

dy/dx = [2y^{2} + x^{2} – 2x^{2}]/4xy

dy/dx = (2y^{2} – x^{2}) / 4xy

Therefore, the differential equation representing the family of curves given by (x- a)^{2} + 2y^{2} = a^{2} is (2y^{2} – x^{2}) / 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.

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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.