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.Â
Â
1.Â

Ans. Given:Â
The highest order derivative present in the differential equation isÂ
 and its order is 4.
The given differential equation is not a polynomial equation in derivatives as the termÂ
 is a T-function of derivativeÂ
 Therefore the degree is not defined.
Hence, order is 4 and degree is not defined.


The given differential equation is not a polynomial equation in derivatives as the termÂ


Hence, order is 4 and degree is not defined.
2.Â
Â
Ans. Given:Â
The highest order derivative present in the differential equation isÂ
 and its order is 1.
The given differential equation is a polynomial equation in derivative
 and the highest power raised to highest order derivativeÂ
 is one, so its degree is 1.
Hence, order is 1 and degree is 1.


The given differential equation is a polynomial equation in derivative


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



Hence, order is 2 and degree is 1.
4.Â
Â
Ans. Given:Â
The highest order derivative present in the differential equation isÂ
 and its order is 2.
The given differential equation is not a polynomial equation in derivatives as the termÂ
 is a T-function of derivativeÂ
 Therefore the degree is not defined.
Hence, order is 2 and degree is not defined.


The given differential equation is not a polynomial equation in derivatives as the termÂ


Hence, order is 2 and degree is not defined.
5.Â
Ans. Given:Â
The highest order derivative present in the differential equation isÂ
 and its order is 2.
The given differential equation is a polynomial equation in derivatives and the highest power raised to highest orderÂ
 is one, so its degree is 1.
Hence, order is 2 and degree is 1.


The given differential equation is a polynomial equation in derivatives and the highest power raised to highest orderÂ

Hence, order is 2 and degree is 1.
6.Â
Â
Ans. Given:Â
The highest order derivative present in the differential equation isÂ
 and its order is 3.
The given differential equation is a polynomial equation in derivatives and the highest power raised to highest orderÂ
 is two, so its degree is 2.
Hence, order is 3 and degree is 2.


The given differential equation is a polynomial equation in derivatives and the highest power raised to highest orderÂ

Hence, order is 3 and degree is 2.
7.Â
Â
Ans. Given:Â
The highest order derivative present in the differential equation isÂ
 and its order is 3.
The given differential equation is a polynomial equation in derivativesÂ
 andÂ
 and the highest power raised to highest orderÂ
 is two, so its degree is 1.
Hence, order is 3 and degree is 1.


The given differential equation is a polynomial equation in derivativesÂ



Hence, order is 3 and degree is 1.
8.Â
Â
Ans. Given:Â
The highest order derivative present in the differential equation isÂ
 and its order is 1.
The given differential equation is a polynomial equation in derivativeÂ
. It may be noted thatÂ
 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 derivativeÂ
 is one so its degree is one.
Hence, order is 1 and degree is 1.


The given differential equation is a polynomial equation in derivativeÂ



Hence, order is 1 and degree is 1.
9.Â
Â
Ans. Given:Â
The highest order derivative present in the differential equation isÂ
 and its order is 2.
The given differential equation is a polynomial equation in derivativesÂ
 andÂ
 and the highest power raised to highest orderÂ
 is one, so its degree is 1.
Hence, order is 2 and degree is 1.


The given differential equation is a polynomial equation in derivativesÂ



Hence, order is 2 and degree is 1.
10.Â
Â
Ans. Given:Â
The highest order derivative present in the differential equation isÂ
 and its order is 2.
The given differential equation is a polynomial equation in derivativeÂ
 andÂ
. It may be noted thatÂ
 is not a polynomial function ofÂ
, it is a T-function ofÂ
 but is not a T-function of derivatives and the highest power raised to highest order derivativeÂ
 is one so its degree is one.
Hence, order is 2 and degree is 1.


The given differential equation is a polynomial equation in derivativeÂ






Hence, order is 2 and degree is 1.
11. The degree of the differential equationÂ
 is:
(A) 3
(B) 2
(C) 1
(D) Not defined
Ans. Given:Â
 ……….(i)This equation is not a polynomial in derivatives asÂ
 is a T-function of derivativeÂ

Therefore, degree of given equation is not defined.
Hence, option (D) is correct.



Therefore, degree of given equation is not defined.
Hence, option (D) is correct.
12. The order of the differential equationÂ
 is:
(A) 2
(B) 1
(C) 0
(D) Not defined
Ans. Given:Â
The highest order derivative present in the differential equation isÂ
 and its order is 2.
Therefore, option (A) is correct.


Therefore, option (A) is correct.