NCERT Solutions for Maths Class 12 Exercise 9.1

Hello Students. In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 9.1.

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NCERT Solutions for Maths Class 12 Exercise 9.2

NCERT Solutions for Maths Class 12 Exercise 9.3

NCERT Solutions for Maths Class 12 Exercise 9.4

NCERT Solutions for Maths Class 12 Exercise 9.5

NCERT Solutions for Maths Class 12 Exercise 9.1

Determine order and degree (if defined) of the differential equations given in Exercises 1 to 10.

Maths Class 12 Ex 9.1 Question 1.

Solution:

The given differential equation is

The highest order derivative present in this differential equation is d⁴y/dx⁴ and its order is 4. So, the order of the differential equation is 4.

The given differential equation is not a polynomial equation in derivatives as the term sin (y’’’) is a trigonometric function of derivative y’’’. Therefore, the degree is not defined.

Hence, the order of the given differential equation is 4 and its degree is not defined.

Maths Class 12 Ex 9.1 Question 2.

y’ + 5y = 0

Solution:

The given differential equation is y’ + 5y = 0

The highest order derivative present in this differential equation is y’ and its order is 1. So, the order of the differential equation is 1.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative y’ is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 1 and its degree is 1.

Maths Class 12 Ex 9.1 Question 3.

Solution:

The given differential equation is

The highest order derivative present in this differential equation is d²s/dt² and its order is 2. So, the order of the differential equation is 2.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative d²s/dt² is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 2 and its degree is 1.

Maths Class 12 Ex 9.1 Question 4.

Solution:

The given differential equation is

The highest order derivative present in this differential equation is d²y/dx² and its order is 2. So, the order of the differential equation is 2.

The given differential equation is not a polynomial equation in derivatives as the term cos (dy/dx) is a trigonometric function of derivative dy/dx. Therefore, the degree is not defined.

Hence, the order of the given differential equation is 2 and its degree is not defined.

Maths Class 12 Ex 9.1 Question 5.

Solution:

The given differential equation is

The highest order derivative present in this differential equation is d²y/dx² and its order is 2. So, the order of the differential equation is 2.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative d²y/dx² is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 2 and its degree is 1.

Maths Class 12 Ex 9.1 Question 6.

(y’’’)² + (y’’)³ + (y’)⁴ + y⁵ = 0

Solution:

The given differential equation is (y’’’)² + (y’’)³ + (y’)⁴ + y⁵ = 0

The highest order derivative present in this differential equation is y’’’ and its order is 3. So, the order of the differential equation is 3.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative y’’’ is 2. Therefore, its degree is 2.

Hence, the order of the given differential equation is 3 and its degree is 2.

Maths Class 12 Ex 9.1 Question 7.

y’’’ + 2y’’ + y’ = 0

Solution:

The given differential equation is y’’’ + 2y’’ + y’ = 0

The highest order derivative present in this differential equation is y’’’ and its order is 3. So, the order of the differential equation is 3.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative y’’’ is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 3 and its degree is 1.

Maths Class 12 Ex 9.1 Question 8.

y’ + y = e^x

Solution:

The given differential equation is y’ + y = e^x

The highest order derivative present in this differential equation is y’ and its order is 1. So, the order of the differential equation is 1.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative y’ is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 1 and its degree is 1.

Maths Class 12 Ex 9.1 Question 9.

y’’ + (y’)² + 2y = 0

Solution:

The given differential equation is y’’ + (y’)² + 2y = 0

The highest order derivative present in this differential equation is y’’ and its order is 2. So, the order of the differential equation is 2.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative y’’ is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 2 and its degree is 1.

Maths Class 12 Ex 9.1 Question 10.

y’’ + 2y’ + sin y = 0

Solution:

The given differential equation is y’’ + 2y’ + sin y = 0

The highest order derivative present in this differential equation is y’’ and its order is 2. So, the order of the differential equation is 2.

The given differential equation is a polynomial equation in derivatives and the highest power raised to the highest order derivative y’’ is 1. Therefore, its degree is 1.

Hence, the order of the given differential equation is 2 and its degree is 1.

Maths Class 12 Ex 9.1 Question 11.

The degree of the differential equation is

(A) 3
(B) 2
(C) 1
(D) not defined

Solution:

The given differential equation is

The given differential equation is not a polynomial equation in derivatives as the term sin (dy/dx) is a trigonometric function of derivative dy/dx. Therefore, the degree is not defined.

Hence, the correct answer is option (D).

Maths Class 12 Ex 9.1 Question 12.

The order of the differential equation is