NCERT Solution Class 12 Chapter 9- Differential Equations Exercise 9.1

The Exercise 9.1 of NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations is based on the following topics:

  1. Introduction to differential equation
  2. Basic Concepts of differential equation
    1. Order of a differential equation
    2. Degree of a differential equation

Solving the problems of this exercise will help the students understand the topics mentioned above in a better way.

Download PDF of NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations Exercise 9.1

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Access Answers of Maths NCERT Class 12 Maths Chapter 9- Differential Equations Exercise 9.1 Page Number 382

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

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 1

Solution:

The given differential equation is,

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 2

⇒ y”” + sin (y’’’) = 0

The highest order derivative present in the differential equation is y’’’’, so its order is three. Hence, the given differential equation is not a polynomial equation in its derivatives and so, its degree is not defined.

2. y’ + 5y = 0

Solution:

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

The highest order derivative present in the differential equation is y’, so its order is one.

Therefore, the given differential equation is a polynomial equation in its derivatives.

So, its degree is one.

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 3

So, its degree is one.

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 4

So, its degree is not defined.

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 5

Therefore, its degree is one.

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 the differential equation is y’’’.

The order is three. Therefore, the given differential equation is a polynomial

equation in y’’’, y’’ and y’.

Then the power raised to y’’’ is 2.

Therefore, its degree is two.

7. y’’’ + 2y’’ + y’ = 0

Solution:

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

The highest order derivative present in the differential equation is y’’’.

The order is three. Therefore, the given differential equation is a polynomial

equation in y’’’, y’’ and y’.

Then the power raised to y’’’ is 1.

Therefore, its degree is one.

8. y’ + y = ex

Solution:

The given differential equation is, y’ + y = ex

= y’ + y – ex = 0

The highest order derivative present in the differential equation is y’.

The order is one. Therefore, the given differential equation is a polynomial equation in y’.

Then the power raised to y’ is 1.

Therefore, its degree is one.

9. y’’’ + (y’)2 + 2y = 0

Solution:

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

The highest order derivative present in the differential equation is y’’.

The order is two. Therefore, the given differential equation is a polynomial equation in y’’ and y’.

Then the power raised to y’’ is 1.

Therefore, its degree is one.

10. y’’’ + 2y’ + sin y = 0

Solution:-

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

The highest order derivative present in the differential equation is y’’.

The order is two. Therefore, the given differential equation is a polynomial equation in y’’ and y’.

Then the power raised to y’’ is 1.

Therefore, its degree is one.

11. The degree of the differential equation.

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 6

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

Solution:-

(D) not defined

The given differential equation is,

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 8
NCERT Solutions for Class 12 Maths Chapter 9 -  Image 7

The highest order derivative present in the differential equation is .

The order is three. Therefore, the given differential equation is not a polynomial.

Therefore, its degree is not defined.

12. The order of the differential equation

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 9

(A) 2 (B) 1 (C) 0 (D) not defined

Solution:-

(A) 2

The given differential equation is,

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 11NCERT Solutions for Class 12 Maths Chapter 9 -  Image 10

The highest order derivative present in the differential equation is .

Therefore, its order is two.

Access other exercise solutions of Class 12 Maths

Exercise 9.2 Solutions 12 Questions

Exercise 9.3 Solutions 12 Questions

Exercise 9.4 Solutions 23 Questions

Exercise 9.5 Solutions 17 Questions

Exercise 9.6 Solutions 19 Questions

Miscellaneous Exercise On Chapter 9 Solutions 18 Questions

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