# NCERT solution class 12 chapter 3 Differential Equations exercise 3.1 mathematics part 2

## EXERCISE 3.1

#### Question 1:

Determine order and degree(if defined) of differential equation  The highest order derivative present in the differential equation is . 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 The given differential equation is: The highest order derivative present in the differential equation is . Therefore, its order is one.

It is a polynomial equation in . The highest power raised to is 1. Hence, its degree is one.

#### Question 3:

Determine order and degree(if defined) of differential equation  The highest order derivative present in the given differential equation is . Therefore, its order is two.

It is a polynomial equation in and . The power raised to is 1.

Hence, its degree is one.

#### Question 4:

Determine order and degree(if defined) of differential equation  The highest order derivative present in the given differential equation is . 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   The highest order derivative present in the differential equation is . Therefore, its order is two.

It is a polynomial equation in and the power raised to is 1.

Hence, its degree is one.

#### Question 6:

Determine order and degree(if defined) of differential equation  The highest order derivative present in the differential equation is . Therefore, its order is three.

The given differential equation is a polynomial equation in .

The highest power raised to is 2. Hence, its degree is 2.

#### Question 7:

Determine order and degree(if defined) of differential equation  The highest order derivative present in the differential equation is . Therefore, its order is three.

It is a polynomial equation in . The highest power raised to is 1. Hence, its degree is 1.

#### Question 8:

Determine order and degree(if defined) of differential equation  The highest order derivative present in the differential equation is . Therefore, its order is one.

The given differential equation is a polynomial equation in and the highest power raised to is one. Hence, its degree is one.

#### Question 9:

Determine order and degree(if defined) of differential equation  The highest order derivative present in the differential equation is . Therefore, its order is two.

The given differential equation is a polynomial equation in and and the highest power raised to is one.

Hence, its degree is one.

#### Question 10:

Determine order and degree(if defined) of differential equation  The highest order derivative present in the differential equation is . Therefore, its order is two.

This is a polynomial equation in and and the highest power raised to is one. Hence, its degree is one.

#### Question 11:

The degree of the differential equation is

(A) 3 (B) 2 (C) 1 (D) not defined 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 The highest order derivative present in the given differential equation is . Therefore, its order is two. 