# NCERT Solutions class 12 Maths Exercise 9.6

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## NCERT Solutions class 12 Maths Differential Equations

In each of the following differential equations given in each Questions 1 to 4, find the general solution:

1.

Ans. Given: Differential equation

Comparing with , we have P = 3 and Q = .

I.F. =

Solution is (I.F.) =

……….(i)

Applying product rule,   I =

Again applying product rule,  I =

I =

I =

I =

Putting the value of I in eq. (i),

2.

Ans. Given: Differential equation

Comparing with , we have P = 2 and Q = .

I.F. =

Solution is (I.F.) =

3.

Ans. Given: Differential equation

Comparing with , we have P =  and Q = .

I.F. =

Solution is (I.F.) =

4.

Ans. Given: Differential equation

Comparing with , we have P =  and Q = .

I.F. =

Solution is (I.F.) =

For each of the following differential equations given in Question 5 to 8, find the general solution:

5.

Ans. Given: Differential equation

Comparing with , we have P =  and Q = .

I.F. =

Solution is (I.F.) =

…….(i)

Putting  and differentiating

Applying product rule,

Putting this value in eq. (i),

6.

Ans. Given: Differential equation

Comparing with , we have P =  and Q = .

I.F. =

Solution is (I.F.) =

7.

Ans. Given: Differential equation

Comparing with , we have P =  and Q = .

I.F. =

Solution is (I.F.) =

Applying Product rule of Integration,

8.

Ans. Given: Differential equation

[to make  unity]

Comparing with , we have P =  and Q = .

I.F. =

Solution is (I.F.) =

For each of the following differential equations given in Question 9 to 12, find the general solution:

9.

Ans. Given: Differential equation

Comparing with , we have P =  and Q = .

=

I.F. =

Solution is (I.F.) =

Applying product rule of Integration,

=

### 10.

Ans. Given: Differential equation

Comparing with , we have P =  and Q = .

I.F. =

Solution is (I.F.) =

Applying product rule of Integration,

=   =

### 11.

Ans. Given: Differential equation

Comparing with , we have P =  and Q = .

I.F. =

Solution is (I.F.) =

### 12.

Ans. Given: Differential equation

Comparing with , we have P =  and Q = .

I.F. =

Solution is (I.F.) =

### For each of the differential equations given in Questions 13 to 15, find a particular solution satisfying the given condition:

13.  when

Ans. Given: Differential equation   when

Comparing with , we have P =  and Q = .

I.F.=

Solution is (I.F.) =

### 14.  when

Ans. Given: Differential equation   when

Comparing with , we have P =  and Q = .

I.F.=

Solution is (I.F.) =

……….(i)

Now putting

Putting the value of  in eq. (i),

### 15.  when

Ans. Given: Differential equation

Comparing with , we have P =  and Q = .

I.F.=

Solution is (I.F.) =

……….(i)

Now putting  in eq. (i),

Putting  in eq. (i),

### 16. Find the equation of the curve passing through the origin, given that the slope of the tangent to the curve at any point  is equal to the sum of coordinates of that point.

Ans. Slope of the tangent to the curve at any point  = Sum of coordinates of the point

Comparing with , we have P =  and Q = .

I.F.=

Solution is (I.F.) =

Applying Product rule of Integration,

……….(i)

Now, since curve (i) passes through the origin (0, 0), therefore putting  in eq. (i)

Putting  in eq. (i),

### 17. Find the equation of the curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangents to the curve at that point by 5.

Ans.    According to the question, Sum of the coordinates of any point say  on the curve

= Magnitude of the slope of the tangent to the curve + 5

Comparing with , we have P =  and Q = .

I.F.=

Solution is (I.F.) =

Applying Product rule of Integration,

……….(i)

Now, since curve (i) passes through the point (0, 2), therefore putting  in eq. (i)

Putting  in eq. (i),

### 18. Choose the correct answer:

The integrating factor of the differential equation  is:

(A)

(B)

(C)

(D)

Ans.    Given: Differential equation

Comparing with , we have P =  and Q = .

I.F.=

Therefore, option (C) is correct.

### 19. Choose the correct answer:

The integrating factor of the differential equation

(A)

(B)

(C)

(D)

Ans. Given: Differential equation

Comparing with , we have P =  and Q =

=

I.F. =

Therefore, option (A) is correct.

## NCERT Solutions class 12 Maths Exercise 9.6

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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### 5 thoughts on “NCERT Solutions class 12 Maths Exercise 9.6”

1. Good job

2. In answer No. 19 in the differential equation there is dy/dx given but they treated it as dx/dy … How is it possible

3. best

4. Thank you sir so much

5. Thanku for provide easy methods of answer