## NCERT Solutions for Class 12 Maths Exercise 9.2 Chapter 9 Differential Equations – FREE PDF Download

Free PDF download of NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.2 (Ex 9.2) and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 12 Maths Chapter 9 Differential Equations Exercise 9.2 Questions with Solutions to help you to revise complete Syllabus and Score More marks.

# NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations (Ex 9.2) Exercise 9.2

In each of the Questions 1 to 6 verify that the given functions (explicit) is a solution of the corresponding differential equation:

1.

**Ans.**Given: ……….(i)

To prove: y is a solution of the differential equation ……….(ii)

Proof: From eq. (i), and

∴∴L.H.S. of eq. (ii), = R.H.S.

Hence, y given by eq. (i) is a solution of .

### 2.

**Ans.**Given: ……….(i)

To prove: y is a solution of the differential equation ……….(ii)

Proof:From, eq. (i),

L.H.S. of eq. (ii),

=

=

= = R.H.S.

Hence, y given by eq. (i) is a solution of .

### 3.

**Ans.**Given: ……….(i)

To prove: y is a solution of the differential equation ……….(ii)

Proof: From eq. (i),

L.H.S. of eq. (ii),

= R.H.S.

Hence, y given by eq. (i) is a solution of .

### 4.

**Ans.**Given: ……….(i)

To prove:y is a solution of the differential equation ……….(ii)

Proof: From eq. (i),

= =

= ………(iii)

Now R.H.S. of eq. (ii)

=

= [From eq. (i)]

= =

L.H.S. = R.H.S

Hence, y given by eq. (i) is a solution of .

### 5.

**Ans.**Given: ……….(i)

To prove:y given by eq. (i) is a solution of differential equation ……….(ii)

Proof: From eq. (i)

L.H.S. of eq. (ii)

= = = = R.H.S. of eq. (ii)

y given by eq. (i) is a solution of differential equation .

### 6.

**Ans.**Given: ……….(i)

To prove:y given by eq. (i) is a solution of differential equation ..(ii)

Proof: From eq. (i),

=

L.H.S. of eq. (ii)

=

R.H.S. of eq. (ii)

=

= [From eq. (i)]

=

=

=

=

=

L.H.S. = R.H.S

Hence, y given by eq. (i) is a solution of .

### In each of the questions 7 to 10, verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

7.

**Ans.**Given: ……….(i)

To prove:y given by eq. (i) is a solution of differential equation …….(ii)

Proof: Differentiating both sides of eq. (i) w.r.t x, we have

⟹y′=−y2xy−1⟹y′=−y2xy−1

Hence, Function (implicit) given by eq. (i) is a solution of .

### 8.

**Ans.**Given: ……….(i)

To prove: y given by eq. (i) is a solution of differential equation

……….(ii)

Proof: Differentiating both sides of eq. (i) w.r.t x, we have

……….(iii)

Putting the value of x from eq. (i) and value of y’ from eq. (iii) in L.H.S. of eq. (ii),

= R.H.S. of (ii)

Hence, Function given by eq. (i) is a solution of .

### 9.

**Ans.**Given: ……….(i)

To prove:y given by eq. (i) is a solution of differential equation ….(ii)

Proof: Differentiating both sides of eq. (i) w.r.t x we have

= eq. (ii)

Hence, Function given by eq. (i) is a solution of

### 10.

**Ans.**Given: ……….(i)

To prove:y given by eq. (i) is a solution of differential equation ……(ii)

Proof: From eq. (i),

dydxdydx=

= ……….(iii)

Putting the values of y and from eq. (i) and (iii) in L.H.S. of eq. (ii),

=

=

= = R.H.S. of eq. (ii)

Hence, Function given by eq. (i) is a solution of .

### Choose the correct answer:

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

**Ans.**Option (D) is correct.

The number of arbitrary constants ( etc.) in the general solution of a differential equation of order is

### 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

**Ans.**The number of arbitrary constants in a particular solution of a differential equation of any order is zero (0) as a particular solution is a solution which contains no arbitrary constant.

Therefore, option (D) is correct.