NCERT Solutions class 12 Maths Exercise 9.1

NCERT Solutions class 12 Maths Exercise 9.1 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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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