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

EXERCISE 3.1


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.

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.

It is a polynomial equation in. 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.

It is a polynomial equation inand. 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.

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.

It is a polynomial equation inand 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.

The given differential equation is a polynomial equation in.

The highest power raised tois 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.

It is a polynomial equation in. 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.

The given differential equation is a polynomial equation inand 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.

The given differential equation is a polynomial equation inandand 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.

This is a polynomial equation inandand 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.

Hence, the correct answer is A.


 

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