NCERT Solutions class 12 Maths Exercise 9.6

NCERT Solutions class 12 Maths Exercise 9.6 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.

Download NCERT solutions for Differential Equations  as PDF.

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),

 

 

 

 

 

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2.  

Ans. Given: Differential equation 

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

       I.F. =

Solution is (I.F.) =

 

 

 

 

 

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3.  

Ans. Given: Differential equation 

Comparing with , we have P =  and Q = .

       I.F. =

Solution is (I.F.) =

 

 

 

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4.

Ans. Given: Differential equation 

Comparing with , we have P =  and Q = .

 

I.F. =

Solution is (I.F.) =

 

 

 

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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),

 

 

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6.  

Ans. Given: Differential equation      

Comparing with , we have P =  and Q = .

       I.F. =

Solution is (I.F.) =

 

 

 

 

 

 

 

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7.  

Ans. Given: Differential equation     

Comparing with , we have P =  and Q = .

 

I.F. =

Solution is (I.F.) =

 

Applying Product rule of Integration,  

 

 

 

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8.  

Ans. Given: Differential equation 

 

       [to make  unity]

Comparing with , we have P =  and Q = .

 

I.F. =

Solution is (I.F.) =

 

 

 

 

 

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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,

   =

 

 

 

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10.  

Ans. Given: Differential equation       

 

Comparing with , we have P =  and Q = .

       I.F. =

Solution is (I.F.) =

 

Applying product rule of Integration,

   =   =

   

      

               

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NCERT Solutions class 12 Maths Exercise 9.6

11.  

Ans. Given: Differential equation      

 

 

Comparing with , we have P =  and Q = .

 

I.F. =

Solution is (I.F.) =

 

 

 

 

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NCERT Solutions class 12 Maths Exercise 9.6

12.  

Ans. Given: Differential equation 

  

 

 

Comparing with , we have P =  and Q = .

 

I.F. =

Solution is (I.F.) =

 

   

  

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NCERT Solutions class 12 Maths Exercise 9.6

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.) =

 

 

 

 

 

 

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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),

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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),   

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NCERT Solutions class 12 Maths Exercise 9.6

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),   

 

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NCERT Solutions class 12 Maths Exercise 9.6

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), 

 

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NCERT Solutions class 12 Maths Exercise 9.6

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.

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NCERT Solutions class 12 Maths Exercise 9.6

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

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