The Exercise 9.1 of NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations is based on the following topics:
- Introduction to differential equation
- Basic Concepts of differential equation
- Order of a differential equation
- Degree of a differential equation
Solving the problems of this exercise will help the students understand the topics mentioned above in a better way.
Download PDF of NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations Exercise 9.1
Access Answers of Maths NCERT Class 12 Maths Chapter 9- Differential Equations Exercise 9.1 Page Number 382
Determine order and degree (if defined) of differential equations given in Exercises 1 to 10
Solution:
The given differential equation is,
⇒ y”” + sin (y’’’) = 0
The highest order derivative present in the differential equation is y’’’’, so its order is three. Hence, the given differential equation is not a polynomial equation in its derivatives and so, its degree is not defined.
2. y’ + 5y = 0
Solution:
The given differential equation is, y’ + 5y = 0
The highest order derivative present in the differential equation is y’, so its order is one.
Therefore, the given differential equation is a polynomial equation in its derivatives.
So, its degree is one.
So, its degree is one.
So, its degree is not defined.
Therefore, its degree is one.
6. (y’’’)2 + (y’’)3 + (y’)4 + y5= 0
Solution:
The given differential equation is, (y’’’)2 + (y’’)3 + (y’)4 + y5= 0
The highest order derivative present in the differential equation is y’’’.
The order is three. Therefore, the given differential equation is a polynomial
equation in y’’’, y’’ and y’.
Then the power raised to y’’’ is 2.
Therefore, its degree is two.
7. y’’’ + 2y’’ + y’ = 0
Solution:
The given differential equation is, y’’’ + 2y’’ + y’ = 0
The highest order derivative present in the differential equation is y’’’.
The order is three. Therefore, the given differential equation is a polynomial
equation in y’’’, y’’ and y’.
Then the power raised to y’’’ is 1.
Therefore, its degree is one.
8. y’ + y = ex
Solution:
The given differential equation is, y’ + y = ex
= y’ + y – ex = 0
The highest order derivative present in the differential equation is y’.
The order is one. Therefore, the given differential equation is a polynomial equation in y’.
Then the power raised to y’ is 1.
Therefore, its degree is one.
9. y’’’ + (y’)2 + 2y = 0
Solution:
The given differential equation is, y’’’ + (y’)2 + 2y = 0
The highest order derivative present in the differential equation is y’’.
The order is two. Therefore, the given differential equation is a polynomial equation in y’’ and y’.
Then the power raised to y’’ is 1.
Therefore, its degree is one.
10. y’’’ + 2y’ + sin y = 0
Solution:-
The given differential equation is, y’’’ + 2y’ + sin y = 0
The highest order derivative present in the differential equation is y’’.
The order is two. Therefore, the given differential equation is a polynomial equation in y’’ and y’.
Then the power raised to y’’ is 1.
Therefore, its degree is one.
11. The degree of the differential equation.
(A) 3 (B) 2 (C) 1 (D) not defined
Solution:-
(D) not defined
The given differential equation is,
The highest order derivative present in the differential equation is .
The order is three. Therefore, the given differential equation is not a polynomial.
Therefore, its degree is not defined.
12. The order of the differential equation
(A) 2 (B) 1 (C) 0 (D) not defined
Solution:-
(A) 2
The given differential equation is,
The highest order derivative present in the differential equation is .
Therefore, its order is two.
Access other exercise solutions of Class 12 Maths
Exercise 9.2 Solutions 12 Questions
Exercise 9.3 Solutions 12 Questions
Exercise 9.4 Solutions 23 Questions
Exercise 9.5 Solutions 17 Questions
Exercise 9.6 Solutions 19 Questions
Miscellaneous Exercise On Chapter 9 Solutions 18 Questions