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# NCERT Solutions class 12 Maths Exercise 9.2

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## NCERT Solutions class 12 Maths Differential Equations

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

Proof: From eq. (i),  and

L.H.S. of eq. (ii), = R.H.S.

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

2.

Ans. Given: ……….(i)

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

Proof:From, eq. (i),

L.H.S. of eq. (ii), =

= = R.H.S.

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

3.

Ans. Given: ……….(i)

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

Proof: From eq. (i),

L.H.S. of eq. (ii), = R.H.S.

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

4.

Ans. Given: ……….(i)

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

Proof: From eq. (i),

=  =  =  ………(iii)

NowR.H.S. of eq. (ii) =  =  [From eq. (i)]

=  =

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

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

5.

Ans. Given: ……….(i)

To prove: 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)

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

6.

Ans. Given: ……….(i)

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

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

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

#### 8.

Ans. Given: ……….(i)

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

……….(ii)

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

……….(iii)

Putting the value of  from eq. (i) and value of  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: given by eq. (i) is a solution of differential equation  ….(ii)

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

= eq. (ii)

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

#### 10.

Ans. Given: ……….(i)

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

Proof: From eq. (i), =

=  ……….(iii)

Putting the values of  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 .

### NCERT Solutions class 12 Maths Exercise 9.2

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.

## NCERT Solutions class 12 Maths Exercise 9.2

NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 20 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide

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