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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,

= =

### 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.) =

### 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.) =

### 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.) =

**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),

### 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),

### 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),

### 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.

### 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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Good job

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

Thank you sir so much