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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

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