## NCERT Solutions for Class 12 Maths Exercise 9.1 Chapter 9 Differential Equations â€“ FREE PDF Download

Free PDF download of NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1 (Ex 9.1) and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 12 Maths Chapter 9 Differential Equations Exercise 9.1 Questions with Solutions to help you to revise complete Syllabus and Score More marks.

# NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations (Ex 9.1) Exercise 9.1

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

**1.Â**

**Â**

**Ans.Â**Given:Â The highest order derivative present in the differential equation isÂ Â and its order is 4.

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

Hence, order is 4 and degree is not defined.

###
**2.Â **
**Â **

**Ans.Â**Given:Â The highest order derivative present in the differential equation isÂ Â and its order is 1.

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

Hence, order is 1 and degree is 1.

###
**3.Â **
**Â **

**Ans.Â**Given:Â The highest order derivative present in the differential equation isÂ Â and its order is 2. The given differential equation is a polynomial equation in derivatives and the highest power raised to highest order derivativeÂ Â is one, so its degree is 1.

Hence, order is 2 and degree is 1.

###
**4.Â **
**Â **

**Ans.Â**Given:Â The highest order derivative present in the differential equation isÂ Â and its order is 2.

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

Hence, order is 2 and degree is not defined.

###
**5.Â **

**Ans.Â**Given:Â The highest order derivative present in the differential equation isÂ Â and its order is 2.

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

Hence, order is 2 and degree is 1.

###
**6.Â **
**Â **

**Ans.Â**Given:Â The highest order derivative present in the differential equation isÂ Â and its order is 3.

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

Hence, order is 3 and degree is 2.

###
**7.Â **
**Â **

**Ans.Â**Given:Â The highest order derivative present in the differential equation isÂ Â and its order is 3.

The given differential equation is a polynomial equation in derivativesÂ Â andÂ Â and the highest power raised to highest orderÂ Â is two, so its degree is 1.

Hence, order is 3 and degree is 1.

###
**8.Â **
**Â **

**Ans.Â**Given:Â The highest order derivative present in the differential equation isÂ Â and its order is 1.

The given differential equation is a polynomial equation in derivativeÂ . It may be noted thatÂ Â 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 derivativeÂ Â is one so its degree is one.

Hence, order is 1 and degree is 1.

###
**9.Â **
**Â **

**Ans.Â**Given:Â The highest order derivative present in the differential equation isÂ Â and its order is 2.

The given differential equation is a polynomial equation in derivativesÂ Â andÂ Â and the highest power raised to highest orderÂ Â is one, so its degree is 1.

Hence, order is 2 and degree is 1.

###
**10.Â **
**Â **

**Ans.Â**Given:Â The highest order derivative present in the differential equation isÂ Â and its order is 2.

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

Hence, order is 2 and degree is 1.

###
**11. The degree of the differential equationÂ **
**Â is:**

**(A) 3**

**(B) 2**

**(C) 1**

**(D) Not defined**

**Ans.Â**Given:Â Â â€¦â€¦â€¦.(i)This equation is not a polynomial in derivatives asÂ Â is a T-function of derivativeÂ

Therefore, degree of given equation is not defined.

Hence, option (D) is correct.

###
**12. The order of the differential equationÂ **
**Â is:**

**(A) 2**

**(B) 1**

**(C) 0**

**(D) Not defined**

**Ans.Â**Given:Â The highest order derivative present in the differential equation isÂ Â andÂ its order is 2.

Therefore, option (A) is correct.