NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations Ex 9.1
Page No 382:
Question 1:
Determine order and degree(if defined) of differential equation 
Answer:
The highest order derivative present in the differential equation is
. Therefore, its order is four.
. Therefore, its order is four.
The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.
Question 2:
Determine order and degree(if defined) of differential equation 
Answer:
The given differential equation is:
The highest order derivative present in the differential equation is
. Therefore, its order is one.
. Therefore, its order is one.
It is a polynomial equation in. The highest power raised tois 1. Hence, its degree is one.
. The highest power raised tois 1. Hence, its degree is one.Question 3:
Determine order and degree(if defined) of differential equation 
Answer:
The highest order derivative present in the given differential equation is
. Therefore, its order is two.
. Therefore, its order is two.
It is a polynomial equation inand
. The power raised tois 1.
and. The power raised tois 1.
Hence, its degree is one.
Question 4:
Determine order and degree(if defined) of differential equation 
Answer:
The highest order derivative present in the given differential equation is
. Therefore, its order is 2.
. Therefore, its order is 2.
The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.
Question 5:
Determine order and degree(if defined) of differential equation 
Answer:
The highest order derivative present in the differential equation is
. Therefore, its order is two.
. Therefore, its order is two.
It is a polynomial equation inand the power raised tois 1.
and the power raised tois 1.
Hence, its degree is one.
Question 6:
Determine order and degree(if defined) of differential equation 
Answer:
The highest order derivative present in the differential equation is
. Therefore, its order is three.
. Therefore, its order is three.
The given differential equation is a polynomial equation in
.
.
The highest power raised tois 2. Hence, its degree is 2.
is 2. Hence, its degree is 2.Question 7:
Determine order and degree(if defined) of differential equation 
Answer:
The highest order derivative present in the differential equation is
. Therefore, its order is three.
. Therefore, its order is three.
It is a polynomial equation in
. The highest power raised tois 1. Hence, its degree is 1.
. The highest power raised tois 1. Hence, its degree is 1.Page No 383:
Question 8:
Determine order and degree(if defined) of differential equation 
Answer:
The highest order derivative present in the differential equation is
. Therefore, its order is one.
. Therefore, its order is one.
The given differential equation is a polynomial equation inand the highest power raised tois one. Hence, its degree is one.
and the highest power raised tois one. Hence, its degree is one.Question 9:
Determine order and degree(if defined) of differential equation 
Answer:
The highest order derivative present in the differential equation is
. Therefore, its order is two.
. Therefore, its order is two.
The given differential equation is a polynomial equation inand
and the highest power raised tois one.
andand the highest power raised tois one.
Hence, its degree is one.
Question 10:
Determine order and degree(if defined) of differential equation 
Answer:
The highest order derivative present in the differential equation is
. Therefore, its order is two.
. Therefore, its order is two.
This is a polynomial equation inand
and the highest power raised tois one. Hence, its degree is one.
andand the highest power raised tois one. Hence, its degree is one.Question 11:
The degree of the differential equation
is
(A) 3 (B) 2 (C) 1 (D) not defined
Answer:
The given differential equation is not a polynomial equation in its derivatives. Therefore, its degree is not defined.
Hence, the correct answer is D.
Question 12:
The order of the differential equation
is
(A) 2 (B) 1 (C) 0 (D) not defined
Answer:
The highest order derivative present in the given differential equation is
. Therefore, its order is two.
. Therefore, its order is two.
Hence, the correct answer is A.
