NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1 (Differential Equations)
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1 contains all the questions with detailed solutions. Students are advised to solve these questions for better understanding of the concepts in exercise 9.1.
Krati Saraswat22 Feb, 2024
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NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1 (Differential Equations)
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1 Differential Equations is prepared by the academic team of Physics Wallah. We have prepared NCERT Solutions for all exercise of Chapter 9. Given below is step by step solutions to all questions given in the NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1 Differential Equations.
NCERT Solutions for Class 12 Maths Chapter 9 Miscellaneous Exercise
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1 Overview
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1 cover several important topics. It is highly recommended for students to review each topic thoroughly in order to gain a comprehensive understanding of the concepts taught in the chapter and make optimal use of the provided solutions. These solutions are the result of dedicated efforts by the Physics Wallah teachers aimed at assisting students in grasping the concepts covered in this chapter. By going through and practicing these solutions, the objective is for students to achieve excellent results in their exams effortlessly.NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1
Solve The Following Questions of NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1
Determine order and degree (if defined) of differential equations given in Questions 1 to 10: Question 1.
Solution :
Given:
The highest order derivative present in the differential equation is y'''' and its order is 4.
The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.2
Question 2. y' + 5y = 0 Solution : The given differential equation is: y' + 5y = 0 The highest order derivative present in the differential equation is y'. Therefore, its order is one. It is a polynomial equation in y'. The highest power raised to y'is 1. Hence, its degree is one.NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.3
Question 3.
Solution :
Given:
The highest order derivative present in the given differential equation is d
2
s/dt
2
Therefore, its order is two.
It is a polynomial equation in d
2
s/dt
2
and ds/dt. The power raised to d
2
s/dt
2
is 1.
Hence, its degree is one.
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.4
Question 4.
Solution :
Given:
The highest order derivative present in the given differential equation is d
2
y/dx
2
Therefore, its order is 2.
The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5
Question 5.
Solution :
Given:
The highest order derivative present in the differential equation is d
2
y/dx
2
and its order is 2.
The given differential equation is a polynomial equation in derivatives and the highest power raised to highest order d
2
y/dx
2
is one, so its degree is 1.
Hence, order is 2 and degree is 1.
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.6
Question 6.
Solution :
Given:
The highest order derivative present in the differential equation is y'''. Therefore, its order is three.
The given differential equation is a polynomial equation in y''', y'', and y'.
The highest power raised to y''' is 2. Hence, its degree is 2.
Question
7.
y''' + 2y'' + y' = 0
Solution :
Given: y''' + 2y'' + y' = 0
The highest order derivative present in the differential equation is y'''. Therefore, its order is three.
It is a polynomial equation in y''', y'' and y'. The highest power raised to y'''is 1. Hence, its degree is 1.
Question
8.
y′ + y = e
x
Solution :
Given: y′ + y = e
x
⇒ y′ + y - e
x
= 0
The highest order derivative present in the differential equation is y'. Therefore, its order is one.
The given differential equation is a polynomial equation in y' and the highest power raised to y' is one. Hence, its degree is one.
Question
9.
y'′ + (y')
2
+ 2y = 0
Solution :
Given: y'′ + (y')
2
+ 2y = 0
The highest order derivative present in the differential equation is y''. Therefore, its order is two.
The given differential equation is a polynomial equation in y''and y' and the highest power raised to y'' is one.
Hence, its degree is one.
Question
10.
y'′ + 2y' + sin y = 0
Solution :
Given: y'′ + 2y' + sin y = 0
The highest order derivative present in the differential equation is y''. Therefore, its order is two.
This is a polynomial equation in y''. and y'.and the highest power raised to y''. is one. Hence, its degree is one.
Question
11. The degree of the differential equation is:
(A) 3
(B) 2
(C) 1
(D) Not defined
Solution :
Given:
……….(i)
The given differential equation is not a polynomial equation in its derivatives. Therefore, its degree is not defined.
Hence, the correct answer is D.
Hence, option (D) is correct.
Question
12. The order of the differential equation is:
(A) 2
(B) 1
(C) 0
(D) Not defined
Solution :
Given:
The highest order derivative present in the differential equation is d
2
y/dx2 and its order is 2.
Therefore, option (A) is correct.
NCERT Solutions For Class 12 Maths Chapter 9 Exercise 9.1 FAQs
How many exercises are there in differential equations?
There are a total of 113 questions in the NCERT Solutions Class 12 Maths Chapter 9 Differential Equations that are divided among 7 exercises.
What is the concept of differential equation class 12?
In Mathematics, a differential equation is an equation that contains one or more functions with its derivatives.
Is differential equations easy class 12?
In Mathematics, a differential equation is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point. It is mainly used in fields such as physics, engineering, biology and so on.
What classes use differential equations?
The study of differential equations is a wide field in pure and applied mathematics, physics, and engineering.
Who is the father of differential equations?
Isaac Newton is the father of differential equations.
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