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NCERT Solutions class 12 Maths Exercise 9.1 (Ex 9.1) Chapter 9 Differential Equations

NCERT Solutions for Class 12 Maths Exercise 9.1 Chapter 9 Differential Equations – FREE PDF Download

Free PDF download of NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1 (Ex 9.1) and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 12 Maths Chapter 9 Differential Equations Exercise 9.1 Questions with Solutions to help you to revise complete Syllabus and Score More marks.

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations (Ex 9.1) Exercise 9.1



Determine order and degree (if defined) of differential equations given in Questions 1 to 10:

1.  

 

Ans. Given: The highest order derivative present in the differential equation is  and its order is 4.

The given differential equation is not a polynomial equation in derivatives as the term  is a T-function of derivative  Therefore the degree is not defined.

Hence, order is 4 and degree is not defined.


2.  

 

Ans. Given: The highest order derivative present in the differential equation is  and its order is 1.

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

Hence, order is 1 and degree is 1.


3.  

 

Ans. Given: The highest order derivative present in the differential equation is  and its order is 2. The given differential equation is a polynomial equation in derivatives and the highest power raised to highest order derivative  is one, so its degree is 1.

Hence, order is 2 and degree is 1.


4.  

 

Ans. Given: The highest order derivative present in the differential equation is  and its order is 2.

The given differential equation is not a polynomial equation in derivatives as the term  is a T-function of derivative  Therefore the degree is not defined.

Hence, order is 2 and degree is not defined.


5. 

 

Ans. Given: The highest order derivative present in the differential equation is  and its order is 2.

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

Hence, order is 2 and degree is 1.


6.  

 

Ans. Given: The highest order derivative present in the differential equation is  and its order is 3.

The given differential equation is a polynomial equation in derivatives and the highest power raised to highest order  is two, so its degree is 2.

Hence, order is 3 and degree is 2.


7.  

 

Ans. Given: The highest order derivative present in the differential equation is  and its order is 3.

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

Hence, order is 3 and degree is 1.


8.  

 

Ans. Given: The highest order derivative present in the differential equation is  and its order is 1.

The given differential equation is a polynomial equation in derivative . It may be noted that  is an exponential function and not a polynomial function but is not an exponential function of derivatives and the highest power raised to highest order derivative  is one so its degree is one.

Hence, order is 1 and degree is 1.


9.  

 

Ans. Given: The highest order derivative present in the differential equation is  and its order is 2.

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

Hence, order is 2 and degree is 1.


10.  

 

Ans. Given: The highest order derivative present in the differential equation is  and its order is 2.

The given differential equation is a polynomial equation in derivative  and . It may be noted that  is not a polynomial function of , it is a T-function of  but is not a T-function of derivatives and the highest power raised to highest order derivative  is one so its degree is one.

Hence, order is 2 and degree is 1.


11. The degree of the differential equation  is:

(A) 3

(B) 2

(C) 1

(D) Not defined

 

Ans. Given:  ……….(i)This equation is not a polynomial in derivatives as  is a T-function of derivative 

Therefore, degree of given equation is not defined.

Hence, option (D) is correct.


12. The order of the differential equation  is:

(A) 2

(B) 1

(C) 0

(D) Not defined

 

Ans. Given: The highest order derivative present in the differential equation is  and its order is 2.

Therefore, option (A) is correct.