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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.

### NCERT Solutions class 12 Maths Exercise 9.1

**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.

### NCERT Solutions class 12 Maths Exercise 9.1

**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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