NCERT Solutions class 12 Maths Exercise 9.2

NCERT Solutions class 12 Maths Exercise 9.2 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

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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 .

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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 .

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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 .

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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 .

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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 .

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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 .

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NCERT Solutions class 12 Maths Exercise 9.2

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 .

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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 .

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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

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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 .

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NCERT Solutions class 12 Maths Exercise 9.2

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

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NCERT Solutions class 12 Maths Exercise 9.2

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

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