NCERT Solutions for Class 12 Maths Exercise 9.1 Chapter 9 Differential Equations – 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.
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image001.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image002.png)
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.
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image005.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image006.png)
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.
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image008.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image009.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image009.png)
Hence, order is 2 and degree is 1.
4.
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image010.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image011.png)
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. ![](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image014.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image011.png)
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.
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image016.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image017.png)
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.
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image018.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image017.png)
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.
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image020.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image007.png)
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.
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image022.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image023.png)
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.
10.
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image024.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image023.png)
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
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image027.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image028.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image013.png)
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
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image029.png)
![](https://cdn1.coolgyan.org/statics/12/maths/ncert/Ex9.1/image011.png)
Therefore, option (A) is correct.