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## NCERT Solutions class 12 Maths Differential Equations

Determine order and degree (if defined) of differential equations given in Questions 1 to 10:

1.

Ans. Given:

The highest order derivative present in the differential equation is  and its order is 4.

The given differential equation is not a polynomial equation in derivatives as the term  is a T-function of derivative  Therefore the degree is not defined.

Hence, order is 4 and degree is not defined.

##### 2.

Ans. Given:

The highest order derivative present in the differential equation is  and its order is 1.

The given differential equation is a polynomial equation in derivative and the highest power raised to highest order derivative  is one, so its degree is 1.

Hence, order is 1 and degree is 1.

##### 3.

Ans. Given:

The highest order derivative present in the differential equation is  and its order is 2. The given differential equation is a polynomial equation in derivatives and the highest power raised to highest order derivative  is one, so its degree is 1.

Hence, order is 2 and degree is 1.

##### 4.

Ans. Given:

The highest order derivative present in the differential equation is  and its order is 2.

The given differential equation is not a polynomial equation in derivatives as the term  is a T-function of derivative  Therefore the degree is not defined.

Hence, order is 2 and degree is not defined.

##### 5.

Ans. Given:

The highest order derivative present in the differential equation is  and its order is 2.

The given differential equation is a polynomial equation in derivatives and the highest power raised to highest order  is one, so its degree is 1.

Hence, order is 2 and degree is 1.

##### 6.

Ans. Given:

The highest order derivative present in the differential equation is  and its order is 3.

The given differential equation is a polynomial equation in derivatives and the highest power raised to highest order  is two, so its degree is 2.

Hence, order is 3 and degree is 2.

7.

Ans. Given:

The highest order derivative present in the differential equation is  and its order is 3.

The given differential equation is a polynomial equation in derivatives  and  and the highest power raised to highest order  is two, so its degree is 1.

Hence, order is 3 and degree is 1.

##### 8.

Ans. Given:

The highest order derivative present in the differential equation is  and its order is 1.

The given differential equation is a polynomial equation in derivative . It may be noted that  is an exponential function and not a polynomial function but is not an exponential function of derivatives and the highest power raised to highest order derivative  is one so its degree is one.

Hence, order is 1 and degree is 1.

##### 9.

Ans. Given:

The highest order derivative present in the differential equation is  and its order is 2.

The given differential equation is a polynomial equation in derivatives  and  and the highest power raised to highest order  is one, so its degree is 1.

Hence, order is 2 and degree is 1.

### NCERT Solutions class 12 Maths Exercise 9.1

##### 10.

Ans. Given:

The highest order derivative present in the differential equation is  and its order is 2.

The given differential equation is a polynomial equation in derivative  and . It may be noted that  is not a polynomial function of , it is a T-function of  but is not a T-function of derivatives and the highest power raised to highest order derivative  is one so its degree is one.

Hence, order is 2 and degree is 1.

### 11. The degree of the differential equation  is:

(A) 3

(B) 2

(C) 1

(D) Not defined

Ans. Given:  ……….(i)

This equation is not a polynomial in derivatives as  is a T-function of derivative

Therefore, degree of given equation is not defined.

Hence, option (D) is correct.

### 12. The order of the differential equation  is:

(A) 2

(B) 1

(C) 0

(D) Not defined

Ans. Given:

The highest order derivative present in the differential equation is  and its order is 2.

Therefore, option (A) is correct.

## NCERT Solutions class 12 Maths Exercise 9.1

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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