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NCERT Solutions class 12 Maths Exercise 9.2 (Ex 9.2) Chapter 9 Differential Equations

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=y2xy1⟹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.