# NCERT Solutions for Exercise 9.1 Class 12 Maths Chapter 9- Differential Equations

NCERT solutions for exercise 9.1 Class 12 Maths chapter 9 introduces the questions related to differential equations. In the NCERT Class 11 Mathematics Book and also chapter 5 of Class 12 Maths, the concepts of derivatives are discussed. Exercise 9.1 Class 12 Maths gives an idea about equations involving derivatives. NCERT solutions for Class 12 Maths chapter 9 exercise 9.1 give clarity about the concept of degree and order of a differential equation. A few examples are also given in the NCERT Book to understand the same. Here are solutions to Class 12 Maths chapter 9 exercise 9.1 prepared by expert Mathematics faculties. In continuation with the Class 12th Maths chapter 6 exercise 9.1, the NCERT Class 12 chapter differential equations have the following 6 exercises.

**Also check -**

Differential Equations exercise 9.2

Differential Equations exercise 9.3

Differential Equations exercise 9.4

Differential Equations exercise 9.5

Differential Equations exercise 9.6

Differential Equations miscellaneous exercise

## ** ****Differential Equations**** Class 12 Chapter 9 Exercise: 9.1**** **

** Question:1 ** Determine order and degree (if defined) of differential equation ** **

** Answer: **

Given function is

We can rewrite it as

Now, it is clear from the above that, the highest order derivative present in differential equation is

Therefore, the order of the given differential equation is 4

Now, the given differential equation is not a polynomial equation in its derivatives

Therefore, it's a degree is not defined

** Question:2 ** Determine order and degree (if defined) of differential equation

Answer:

Given function is

Now, it is clear from the above that, the highest order derivative present in differential equation is

Therefore, the order of the given differential equation is 1

Now, the given differential equation is a polynomial equation in its derivatives and its highest power raised to y ' is 1

Therefore, it's a degree is 1.

** Question:3 ** Determine order and degree (if defined) of differential equation ** **

** Answer: **

Given function is

We can rewrite it as

Now, it is clear from the above that, the highest order derivative present in differential equation is

Therefore, the order of the given differential equation ** ** is 2

Now, the given differential equation is a polynomial equation in its derivatives and power raised to s '' is 1

Therefore, it's a degree is 1

** Question:4 ** Determine order and degree (if defined) of differential equation.

** Answer: **

Given function is

We can rewrite it as

Now, it is clear from the above that, the highest order derivative present in differential equation is

Therefore, the order of the given differential equation is 2

Now, the given differential equation is not a polynomial equation in its derivatives

Therefore, it's a degree is not defined

** Question:5 ** Determine order and degree (if defined) of differential equation.

** **

** Answer: **

Given function is ** **

Now, it is clear from the above that, the highest order derivative present in differential equation is

Therefore, order of given differential equation is 2

Now, the given differential equation is a polynomial equation in it's dervatives and power raised to is 1

Therefore, it's degree is 1

** Question:6 ** Determine order and degree (if defined) of differential equation ** **

** Answer: **

Given function is

Now, it is clear from the above that, the highest order derivative present in differential equation is

Therefore, order of given differential equation ** ** is 3

Now, the given differential equation is a polynomial equation in it's dervatives and power raised to is 2

Therefore, it's degree is 2

** Question:7 ** Determine order and degree (if defined) of differential equation

** Answer: **

Given function is

Now, it is clear from the above that, the highest order derivative present in differential equation is

Therefore, order of given differential equation is 3

Now, the given differential equation is a polynomial equation in it's dervatives and power raised to is 1

Therefore, it's degree is 1

** Question:8 ** Determine order and degree (if defined) of differential equation

** Answer: **

Given function is ** **

Now, it is clear from the above that, the highest order derivative present in differential equation is

Therefore, order of given differential equation is 1

Now, the given differential equation is a polynomial equation in it's dervatives and power raised to is 1

Therefore, it's degree is 1

** Question:9 ** Determine order and degree (if defined) of differential equation

** Answer: **

Given function is

Now, it is clear from the above that, the highest order derivative present in differential equation is

Therefore, order of given differential equation is 2

Now, the given differential equation is a polynomial equation in it's dervatives and power raised to is 1

Therefore, it's degree is 1

** Question:10 ** Determine order and degree (if defined) of differential equation

** Answer: **

Given function is

Now, it is clear from the above that, the highest order derivative present in differential equation is

Therefore, order of given differential equation is 2

Now, the given differential equation is a polynomial equation in it's dervatives and power raised to is 1

Therefore, it's degree is 1

** Question:11 ** The degree of the differential equation is

(A) 3

(B) 2

(C) 1

(D) not defined

** Answer: **

Given function is

We can rewrite it as

Now, it is clear from the above that, the highest order derivative present in differential equation is

Therefore, order of given differential equation ** ** is 2

Now, the given differential equation is a not polynomial equation in it's dervatives

Therefore, it's degree is not defined

Therefore, answer is (D)

** Question:12 ** The order of the differential equation is

(A) 2

(B) 1

(C) 0

(D) Not Defined

** Answer: **

Given function is

We can rewrite it as

Now, it is clear from the above that, the highest order derivative present in differential equation is

Therefore, order of given differential equation ** ** is 2

Therefore, answer is (A)

**More About NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1**

There is one example prior to exercise 9.1 Class 12 Maths and 12 questions in the Class 12 Maths chapter 9 exercise 9.1. Two questions of Class 12th Maths chapter 6 exercise 9.1 are multiple objective type questions. All the questions in NCERT solutions for Class 12 Maths chapter 9 exercise 9.1 are to find the order and degree of the given differential equations.

**Also Read| **Differential Equations Class 12th Notes

**Benefits of NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1**

One fill in the blank or multiple choice type or very short answer can be expected from exercise 9.1 Class 12 Maths for CBSE Class 12 Maths Board Exams

Not only CBSE, but certain state boards also follow the NCERT Syllabus. Therefore the NCERT solutions for Class 12 Maths chapter 9 exercise 9.1 can be used to prepare for state boards that follow NCERT.

**Also see-**

NCERT Exemplar Solutions Class 12 Maths Chapter 9

NCERT Solutions for Class 12 Maths Chapter 9

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**Subject Wise NCERT Exemplar Solutions**

NCERT Exemplar Class 12 Maths

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