NCERT Solutions for Maths Class 12 Exercise 9.1

NCERT Solutions for Maths Class 12 Exercise 9.1

 

NCERT Solutions for Maths Class 12 Exercise 9.1

 

Hello Students. Welcome to maths-formula.com. In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 9.1.

 

You can download the PDF of NCERT Books Maths Chapter 9 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 9.1.

 

Class 12th is a very crucial stage of your student’s life, since you take all important decisions about your career on this stage. Mathematics plays a vital role to take decision for your career because if you are good in mathematics, you can choose engineering and technology field as your career.

 

NCERT Solutions for Maths Class 12 Exercise 9.1 helps you to solve each and every problem with step by step explanation which makes you strong in mathematics.

 

All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from NCERT Syllabus for Mathematics Class 12.

 

NCERT Solutions for Maths Class 12 Exercise 9.1 are prepared by the experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET level exams, then it will definitely make your foundation strong.

 

If you want to recall All Maths Formulas for Class 12, you can find it by clicking this link.

If you want to recall All Maths Formulas for Class 11, you can find it by clicking this link.


NCERT Solutions for Maths Class 12 Exercise 9.2

 

NCERT Solutions for Maths Class 12 Exercise 9.3

 

NCERT Solutions for Maths Class 12 Exercise 9.4

 

NCERT Solutions for Maths Class 12 Exercise 9.5

 

NCERT Solutions for Maths Class 12 Exercise 9.6


NCERT Solutions for Maths Class 12 Exercise 9.1 


Determine order and degree (if defined) of the differential equations given in Exercises 1 to 10.

Maths Class 12 Ex 9.1 Question 1.

Solution:

The given differential equation is 

The highest order derivative present in this differential equation is d4y/dx4 and its order is 4. So, the order of the differential equation is 4.

The given differential equation is not a polynomial equation in derivatives as the term sin (y’’’) is a trigonometric function of derivative y’’’. Therefore, the degree is not defined.

Hence, the order of the given differential equation is 4 and its degree is not defined.

Maths Class 12 Ex 9.1 Question 2.

y’ + 5y = 0

Solution:

The given differential equation is y’ + 5y = 0

The highest order derivative present in this differential equation is y’ and its order is 1. So, the order of the differential equation is 1.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative y’ is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 1 and its degree is 1.

Maths Class 12 Ex 9.1 Question 3.

Solution:

The given differential equation is 

The highest order derivative present in this differential equation is d2s/dt2 and its order is 2. So, the order of the differential equation is 2.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative d2s/dt2 is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 2 and its degree is 1.

Maths Class 12 Ex 9.1 Question 4.

Solution:

The given differential equation is  

The highest order derivative present in this differential equation is d2y/dx2 and its order is 2. So, the order of the differential equation is 2.

The given differential equation is not a polynomial equation in derivatives as the term cos (dy/dx) is a trigonometric function of derivative dy/dx. Therefore, the degree is not defined.

Hence, the order of the given differential equation is 2 and its degree is not defined.

Maths Class 12 Ex 9.1 Question 5.

Solution:

The given differential equation is 

The highest order derivative present in this differential equation is d2y/dx2 and its order is 2. So, the order of the differential equation is 2.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative d2y/dx2 is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 2 and its degree is 1.

Maths Class 12 Ex 9.1 Question 6.

(y’’’)2 + (y’’)3 + (y’)4 + y5 = 0

Solution:

The given differential equation is (y’’’)2 + (y’’)3 + (y’)4 + y5 = 0

The highest order derivative present in this differential equation is y’’’ and its order is 3. So, the order of the differential equation is 3.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative y’’’ is 2. Therefore, its degree is 2.

Hence, the order of the given differential equation is 3 and its degree is 2.

Maths Class 12 Ex 9.1 Question 7.

y’’’ + 2y’’ + y’ = 0

Solution:

The given differential equation is y’’’ + 2y’’ + y’ = 0

The highest order derivative present in this differential equation is y’’’ and its order is 3. So, the order of the differential equation is 3.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative y’’’ is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 3 and its degree is 1.

Maths Class 12 Ex 9.1 Question 8.

y’ + y = ex

Solution:

The given differential equation is y’ + y = ex

The highest order derivative present in this differential equation is y and its order is 1. So, the order of the differential equation is 1.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative y is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 1 and its degree is 1.

Maths Class 12 Ex 9.1 Question 9.

y’’ + (y’)2 + 2y = 0

Solution:

The given differential equation is y’’ + (y’)2 + 2y = 0

The highest order derivative present in this differential equation is y’’ and its order is 2. So, the order of the differential equation is 2.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative y’’ is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 2 and its degree is 1.

Maths Class 12 Ex 9.1 Question 10.

y’’ + 2y’ + sin y = 0

Solution:

The given differential equation is y’’ + 2y’ + sin y = 0

The highest order derivative present in this differential equation is y’’ and its order is 2. So, the order of the differential equation is 2.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative y’’ is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 2 and its degree is 1.

Maths Class 12 Ex 9.1 Question 11.

The degree of the differential equation is


(A) 3
(B) 2
(C) 1
(D) not defined

Solution:

The given differential equation is 

The given differential equation is not a polynomial equation in derivatives as the term sin (dy/dx) is a trigonometric function of derivative dy/dx. Therefore, the degree is not defined.

Hence, the correct answer is option (D).

Maths Class 12 Ex 9.1 Question 12.

The order of the differential equation is

(A) 2
(B) 1
(C) 0
(D) not defined

Solution:

The given differential equation is 

The highest order derivative present in this differential equation is d2y/dx2 and its order is 2. So, the order of the differential equation is 2.

Hence, the correct answer is option (A).

NCERT Solutions for Maths Class 12 Exercise 9.2

 

NCERT Solutions for Maths Class 12 Exercise 9.3

 

NCERT Solutions for Maths Class 12 Exercise 9.4

 

NCERT Solutions for Maths Class 12 Exercise 9.5

 

NCERT Solutions for Maths Class 12 Exercise 9.6

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