NCERT Solutions for Class 12 Maths Exercise 9.1 Chapter 9 Differential Equations – FREE PDF Download
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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. 
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. 
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.
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.
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.
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.
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.
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.
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.
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.
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
……….(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
The highest order derivative present in the differential equation is and its order is 2.Therefore, option (A) is correct.
