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.