Ncert Solutions For Class 12 Maths Ex 9.2

The Exercise 9.2 of NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations is based on the topic “General and Particular Solutions of a Differential Equation”.The solution which contains arbitrary constants is called the general solution (primitive) of the differential equation. The solution free from arbitrary constants i.e., the solution obtained from the general solution by giving particular values to the arbitrary constants is called a particular solution of the differential equation. Solve the problems present in this exercise to understand these topics better.

Download PDF of NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations Exercise 9.2

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Access Answers of Maths NCERT Class 12 Maths Chapter 9- Differential Equations Exercise 9.2 Page Number 385

In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

1. y = ex + 1 : y″ – y′ = 0

Solution:-

From the question it is given that y = ex + 1

Differentiating both sides with respect to x, we get,

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 12

⇒ y” = ex

Then,

Substituting the values of y’ and y” in the given differential equations, we get,

y” – y’ = ex – ex = RHS.

Therefore, the given function is a solution of the given differential equation.

2. y = x2 + 2x + C : y′ – 2x – 2 = 0

Solution:-

From the question it is given that y = x2 + 2x + C

Differentiating both sides with respect to x, we get,

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 13

y’ = 2x + 2

Then,

Substituting the values of y’ in the given differential equations, we get,

= y’ – 2x -2

= 2x + 2 – 2x – 2

= 0

= RHS

Therefore, the given function is a solution of the given differential equation.

3. y = cos x + C : y′ + sin x = 0

Solution:-

From the question it is given that y = cos x + C

Differentiating both sides with respect to x, we get,

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 14

y’ = -sinx

Then,

Substituting the values of y’ in the given differential equations, we get,

= y’ + sinx

= – sinx + sinx

= 0

= RHS

Therefore, the given function is a solution of the given differential equation.

4. y = √(1 + x2): y’ = ((xy)/(1 + x2))

Solution:-

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 15

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 16

5. y = Ax : xy′ = y (x ≠ 0)

Solution:-

From the question it is given that y = Ax

Differentiating both sides with respect to x, we get,

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 17

y’ = A

Then,

Substituting the values of y’ in the given differential equations, we get,

= xy’

= x × A

= Ax

= Y … [from the question]

= RHS

Therefore, the given function is a solution of the given differential equation

6. y = x sinx : xy’ = y + x (√(x2 – y2)) (x ≠ 0 and x>y or x< – y)

Solution:-

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 18

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 19

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 20

Solution:-

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 21

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 22

8. y – cos y = x : (y sin y + cos y + x) y′ = y

Solution:-

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 23

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 24

9. x + y = tan-1y : y2 y′ + y2 + 1 = 0

Solution:-

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 25

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 26

Therefore, the given function is the solution of the corresponding differential equation.
NCERT Solutions for Class 12 Maths Chapter 9 -  Image 27

Solution:-

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 28

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 29

11. The number of arbitrary constants in the general solution of a differential equation of fourth order are:

(A) 0 (B) 2 (C) 3 (D) 4

Solution:-

(D) 4

The solution which contains arbitrary constants is called the general solution (primitive) of the differential equation.

12. The number of arbitrary constants in the particular solution of a differential equation of third order are:

(A) 3 (B) 2 (C) 1 (D) 0

Solution:-

(D) 0

The solution free from arbitrary constants i.e., the solution obtained from the general solution by giving particular values to the arbitrary constants is called a particular solution of the differential equation.

Access other exercise solutions of Class 12 Maths Chapter 9

Exercise 9.1 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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