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NCERT Solutions for Exercise 9.1 Class 12 Maths Chapter 9- Differential Equations

NCERT Solutions for Exercise 9.1 Class 12 Maths Chapter 9- Differential Equations

Edited By Ramraj Saini | Updated on Dec 04, 2023 08:02 AM IST | #CBSE Class 12th

NCERT Solutions For Class 12 Maths Chapter 9 Exercise 9.1

NCERT Solutions for Exercise 9.1 Class 12 Maths Chapter 9 Differential Equations are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. NCERT solutions for exercise 9.1 Class 12 Maths chapter 9 introduces the questions related to differential equations. In the NCERT Class 11 Mathematics Book and also chapter 5 of Class 12 Maths, the concepts of derivatives are discussed. Exercise 9.1 Class 12 Maths gives an idea about equations involving derivatives. NCERT solutions for Class 12 Maths chapter 9 exercise 9.1 give clarity about the concept of degree and order of a differential equation. A few examples are also given in the NCERT Book to understand the same.

Here are solutions to Class 12 Maths chapter 9 exercise 9.1 prepared by expert Mathematics faculties. 12th class Maths exercise 9.1 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.

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Differential Equations Class 12 Chapter 9 Exercise: 9.1

Question:1 Determine order and degree (if defined) of differential equation \frac{\mathrm{d} ^4y}{\mathrm{d} x^4} +\sin(y''')=0

Answer:

Given function is
\frac{\mathrm{d} ^4y}{\mathrm{d} x^4} +\sin(y''')=0
We can rewrite it as
y^{''''}+\sin(y''') =0
Now, it is clear from the above that, the highest order derivative present in differential equation is y^{''''}

Therefore, the order of the given differential equation \frac{\mathrm{d} ^4y}{\mathrm{d} x^4} +\sin(y''')=0 is 4
Now, the given differential equation is not a polynomial equation in its derivatives
Therefore, it's a degree is not defined

Question:2 Determine order and degree (if defined) of differential equation y' + 5y = 0

Answer:

Given function is
y' + 5y = 0
Now, it is clear from the above that, the highest order derivative present in differential equation is y^{'}
Therefore, the order of the given differential equation y' + 5y = 0 is 1
Now, the given differential equation is a polynomial equation in its derivatives and its highest power raised to y ' is 1
Therefore, it's a degree is 1.

Question:3 Determine order and degree (if defined) of differential equation \left(\frac{\mathrm{d} s}{\mathrm{d} t} \right )^4 + 3s \frac{\mathrm{d}^2 s}{\mathrm{d} t^2} = 0

Answer:

Given function is
\left(\frac{\mathrm{d} s}{\mathrm{d} t} \right )^4 + 3s \frac{\mathrm{d}^2 s}{\mathrm{d} t^2} = 0
We can rewrite it as
(s^{'})^4+3s.s^{''} =0
Now, it is clear from the above that, the highest order derivative present in differential equation is s^{''}

Therefore, the order of the given differential equation \left(\frac{\mathrm{d} s}{\mathrm{d} t} \right )^4 + 3s \frac{\mathrm{d}^2 s}{\mathrm{d} t^2} = 0 is 2
Now, the given differential equation is a polynomial equation in its derivatives and power raised to s '' is 1
Therefore, it's a degree is 1

Question:4 Determine order and degree (if defined) of differential equation.

\left(\frac{d^2y}{dx^2} \right )^2 + \cos\left(\frac{dy}{dx} \right )= 0

Answer:

Given function is
\left(\frac{d^2y}{dx^2} \right )^2 + \cos\left(\frac{dy}{dx} \right )= 0
We can rewrite it as
(y^{''})^2+\cos y^{''} =0
Now, it is clear from the above that, the highest order derivative present in differential equation is y^{''}

Therefore, the order of the given differential equation \left(\frac{d^2y}{dx^2} \right )^2 + \cos\left(\frac{dy}{dx} \right )= 0 is 2
Now, the given differential equation is not a polynomial equation in its derivatives
Therefore, it's a degree is not defined

Question:5 Determine order and degree (if defined) of differential equation.

\frac{d^2y}{dx^2} = \cos 3x + \sin 3x

Answer:

Given function is
\frac{d^2y}{dx^2} = \cos 3x + \sin 3x
\Rightarrow \frac{d^2y}{dx^2}- \cos 3x - \sin 3x = 0
Now, it is clear from the above that, the highest order derivative present in differential equation is y^{''}\left ( \frac{d^2y}{dx^2} \right )

Therefore, order of given differential equation \frac{d^2y}{dx^2}- \cos 3x - \sin 3x = 0 is 2
Now, the given differential equation is a polynomial equation in it's dervatives \frac{d^2y}{dx^2} and power raised to \frac{d^2y}{dx^2} is 1
Therefore, it's degree is 1

Question:6 Determine order and degree (if defined) of differential equation (y''')^2 + (y'')^3 + (y')^4 + y^5= 0

Answer:

Given function is
(y''')^2 + (y'')^3 + (y')^4 + y^5= 0
Now, it is clear from the above that, the highest order derivative present in differential equation is y^{'''}

Therefore, order of given differential equation (y''')^2 + (y'')^3 + (y')^4 + y^5= 0 is 3
Now, the given differential equation is a polynomial equation in it's dervatives y^{'''} , y^{''} \ and \ y^{'} and power raised to y^{'''} is 2
Therefore, it's degree is 2

Question:7 Determine order and degree (if defined) of differential equation

y''' + 2y'' + y' =0

Answer:

Given function is
y''' + 2y'' + y' =0
Now, it is clear from the above that, the highest order derivative present in differential equation is y^{'''}

Therefore, order of given differential equation y''' + 2y'' + y' =0 is 3
Now, the given differential equation is a polynomial equation in it's dervatives y^{'''} , y^{''} \ and \ y^{'} and power raised to y^{'''} is 1
Therefore, it's degree is 1

Question:8 Determine order and degree (if defined) of differential equation

y' + y = e^x

Answer:

Given function is
y' + y = e^x
\Rightarrow y^{'}+y-e^x=0
Now, it is clear from the above that, the highest order derivative present in differential equation is y^{'}

Therefore, order of given differential equation y^{'}+y-e^x=0 is 1
Now, the given differential equation is a polynomial equation in it's dervatives y^{'} and power raised to y^{'} is 1
Therefore, it's degree is 1

Question:9 Determine order and degree (if defined) of differential equation

y'' + (y')^2 + 2y = 0

Answer:

Given function is
y'' + (y')^2 + 2y = 0
Now, it is clear from the above that, the highest order derivative present in differential equation is y^{''}

Therefore, order of given differential equation y'' + (y')^2 + 2y = 0 is 2
Now, the given differential equation is a polynomial equation in it's dervatives y^{''} \ and \ y^{'} and power raised to y^{''} is 1
Therefore, it's degree is 1

Question:10 Determine order and degree (if defined) of differential equation

y'' + 2y' + \sin y = 0

Answer:

Given function is
y'' + 2y' + \sin y = 0
Now, it is clear from the above that, the highest order derivative present in differential equation is y^{''}

Therefore, order of given differential equation y'' + 2y' + \sin y = 0 is 2
Now, the given differential equation is a polynomial equation in it's dervatives y^{''} \ and \ y^{'} and power raised to y^{''} is 1
Therefore, it's degree is 1

Question:11 The degree of the differential equation \left(\frac{d^2y}{dx^2} \right )^3 + \left(\frac{dy}{dx} \right )^2 + \sin\left(\frac{dy}{dx}\right ) + 1= 0 is

(A) 3

(B) 2

(C) 1

(D) not defined

Answer:

Given function is
\left(\frac{d^2y}{dx^2} \right )^3 + \left(\frac{dy}{dx} \right )^2 + \sin\left(\frac{dy}{dx}\right ) + 1= 0
We can rewrite it as
(y^{''})^3+(y^{'})^2+\sin y^{'}+1=0
Now, it is clear from the above that, the highest order derivative present in differential equation is y^{''}

Therefore, order of given differential equation \left(\frac{d^2y}{dx^2} \right )^3 + \left(\frac{dy}{dx} \right )^2 + \sin\left(\frac{dy}{dx}\right ) + 1= 0 is 2
Now, the given differential equation is a not polynomial equation in it's dervatives
Therefore, it's degree is not defined

Therefore, answer is (D)

Question:12 The order of the differential equation 2x^2\frac{d^2y}{dx^2} - 3\frac{dy}{dx} + y = 0 is

(A) 2

(B) 1

(C) 0

(D) Not Defined

Answer:

Given function is
2x^2\frac{d^2y}{dx^2} - 3\frac{dy}{dx} + y = 0
We can rewrite it as
2x.y^{''}-3y^{'}+y=0
Now, it is clear from the above that, the highest order derivative present in differential equation is y^{''}

Therefore, order of given differential equation 2x^2\frac{d^2y}{dx^2} - 3\frac{dy}{dx} + y = 0 is 2

Therefore, answer is (A)

More About NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1

There is one example prior to exercise 9.1 Class 12 Maths and 12 questions in the Class 12 Maths chapter 9 exercise 9.1. Two questions of Class 12th Maths chapter 6 exercise 9.1 are multiple objective type questions. All the questions in NCERT solutions for Class 12 Maths chapter 9 exercise 9.1 are to find the order and degree of the given differential equations.

Also Read| Differential Equations Class 12th Notes

Benefits of NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1

  • One fill in the blank or multiple choice type or very short answer can be expected from exercise 9.1 Class 12 Maths for CBSE Class 12 Maths Board Exams

  • Not only CBSE, but certain state boards also follow the NCERT Syllabus. Therefore the NCERT solutions for Class 12 Maths chapter 9 exercise 9.1 can be used to prepare for state boards that follow NCERT.

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Key Features Of NCERT Solutions for Exercise 9.1 Class 12 Maths Chapter 9

  • Comprehensive Coverage: The solutions encompass all the topics covered in ex 9.1 class 12, ensuring a thorough understanding of the concepts.
  • Step-by-Step Solutions: In this class 12 maths ex 9.1, each problem is solved systematically, providing a stepwise approach to aid in better comprehension for students.
  • Accuracy and Clarity: Solutions for class 12 ex 9.1 are presented accurately and concisely, using simple language to help students grasp the concepts easily.
  • Conceptual Clarity: In this 12th class maths exercise 9.1 answers, emphasis is placed on conceptual clarity, providing explanations that assist students in understanding the underlying principles behind each problem.
  • Inclusive Approach: Solutions for ex 9.1 class 12 cater to different learning styles and abilities, ensuring that students of various levels can grasp the concepts effectively.
  • Relevance to Curriculum: The solutions for class 12 maths ex 9.1 align closely with the NCERT curriculum, ensuring that students are prepared in line with the prescribed syllabus.

Also see-

NCERT Solutions Subject Wise

Subject Wise NCERT Exemplar Solutions

Frequently Asked Questions (FAQs)

1. How many questions are solved in Exercise 9.1 Class 12 Maths?

12 questions and their answers are given in the NCERT solutions for Class 12 Maths chapter 9 exercise 9.1

2. What number of exercises are present in the chapter differential equations?

7 exercises. In which one is miscellaneous exercises.

3. What is the difference between miscellaneous exercises and other exercises given in the chapter?

Miscellaneous exercise covers question from whole chapter and exercise questions covers topics discussed in that particular area.

4. What are the concepts covered in the Class 12th Maths chapter 6 exercise 9.1?

The concepts of order and degree of differential equations are covered in the Class 12 Maths chapter 9 exercise 9.1.

5. How many examples are solved before Class 12th Maths chapter 6 exercise 9.1?

One solved example is given in the NCERT book before exercise 9.1 Class 12 Maths.

6. Is the topic of degree and order important for JEE Main exam?

Yes, Students can expect questions from this part for JEE Mains.

7. Are the NCERT Solutions for Class 12 Maths chapter 9 exercise 9.1 reliable?

Yes, these solutions of exercise 9.1 are prepared by expert faculty and are reviewed.

8. Why do we solve Exercise 9.1 Class 12 Maths?

It is necessary to get clarity over the topics degree and order of a differential equation. NCERT Solutions for Class 12 Maths chapter 9 exercise 9.1 helps for the same. 

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quartely question paper for mathematics cbse

Hello there! Thanks for reaching out to us at Careers360.

Ah, you're looking for CBSE quarterly question papers for mathematics, right? Those can be super helpful for exam prep.

Unfortunately, CBSE doesn't officially release quarterly papers - they mainly put out sample papers and previous years' board exam papers. But don't worry, there are still some good options to help you practice!

Have you checked out the CBSE sample papers on their official website? Those are usually pretty close to the actual exam format. You could also look into previous years' board exam papers - they're great for getting a feel for the types of questions that might come up.

If you're after more practice material, some textbook publishers release their own mock papers which can be useful too.

Let me know if you need any other tips for your math prep. Good luck with your studies!

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Jefferson 25 September,2024
i have taken admission in clg after my campartment exam in chemistry along with the neet 2025 preperation but unfortunately i again got campartment after doing all this preparation i got 15 marks only now I can't able to think what should I do next.

It's understandable to feel disheartened after facing a compartment exam, especially when you've invested significant effort. However, it's important to remember that setbacks are a part of life, and they can be opportunities for growth.

Possible steps:

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Remember: This is a temporary setback. With the right approach and perseverance, you can overcome this challenge and achieve your goals.

I hope this information helps you.







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Kanishka kaushikii 17 September,2024
i scored 84 percent in cbse 2 years ago.Am i eligible for medhavi scholarship if give 12th again after 2 drop years and will got 75+ in mpboard

Hi,

Qualifications:
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Yuvan 30 August,2024
i upload 12th board result screenshot in ncweb form from the cbse site so it is valid

hello mahima,

If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.

hope this helps.

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Ashvadha 12 July,2024
Kya mujhe class 12 ka important question milega jo exam mai per year puche jate hai

Hello Akash,

If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.

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I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.

Thank you and wishing you all the best for your bright future.

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kumardurgesh1802 10 July,2024
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