NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 (Differential Equations)
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 contains all the questions with detailed solutions. Students are advised to solve these questions for better understanding of the concepts in exercise 9.5.
Krati Saraswat16 Jul, 2024
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NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 (Differential Equations)
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 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 of all questions given in the NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5.NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 (Differential Equations) Overview
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 covers these important topics. Students are encouraged to review each topic thoroughly in order to fully understand the concepts taught in the chapter and make optimal use of the provided solutions. These solutions are the outcome of the dedicated effort that the Physics Wallah teachers have been doing to aid students in understanding the ideas covered in this chapter. After going over and rehearsing these responses, the goal is for students to easily score outstanding exam resultsNCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5
Solve The Following Questions of NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5: In each of the following Questions 1 to 5, show that the differential equation is homogenous and solve each of them: Question 1.
Solution : The given differential equation i.e., ( x 2 + xy ) dy = ( x 2 + y 2 ) dx can be written as: 
This shows that equation (1) is a homogeneous equation. To solve it, we make the substitution as: y = vx Differentiating both sides with respect to x , we get: dy/dx = v + x dv/dx Substituting the values of v and dy/dx in equation (1), we get: 
This is the required solution of the given differential equation.Question 2.
Solution : The given differential equation is: 
Thus, the given equation is a homogeneous equation. To solve it, we make the substitution as: y = vx Differentiating both sides with respect to x , we get: dy/dx = v + x dv/dx Substituting the values of y and dy/dx in equation (1), we get: 
This is the required solution of the given differential equationQuestion 3.
Solution : The given differential equation is 
Question 4.
Solution : The given differential equation is: 
Therefore, the given differential equation is a homogeneous equation. To solve it, we make the substitution as: y = vx 
This is the required solution of the given differential equation. Question 5. 
Solution : The given differential equation is: 
Therefore, the given differential equation is a homogeneous equation. To solve it, we make the substitution as: y = vx 
This is the required solution for the given differential equation. In each of the Questions 6 to 10, show that the given differential equation is homogeneous and solve each of them: Question 6. 
Solution : 
Therefore, the given differential equation is a homogeneous equation. To solve it, we make the substitution as: y = vx 
This is the required solution of the given differential equation. Question 7. 
Solution : The given differential equation is: 
Therefore, the given differential equation is a homogeneous equation. To solve it, we make the substitution as: y = vx 
This is the required solution of the given differential equation. Question 8. 
Solution : 
Therefore, the given differential equation is a homogeneous equation. To solve it, we make the substitution as: y = vx 
This is the required solution of the given differential equation. Question 9. 
Solution : 
Therefore, the given differential equation is a homogeneous equation. To solve it, we make the substitution as: y = vx 
Integrating both sides, we get: 
This is the required solution of the given differential equation. Question 10. 
Solution : 
Therefore, the given differential equation is a homogeneous equation. To solve it, we make the substitution as: x = vy 
This is the required solution of the given differential equation. For each of the differential equations in Questions from 11 to 15, find the particular solution satisfying the given condition Question 11. (x + y) dy + (x – y) dx = 0; y = 1 when x = 1 Solution : 
Therefore, the given differential equation is a homogeneous equation. To solve it, we make the substitution as: y = vx 
Substituting the value of 2 k in equation (2), we get: 
This is the required solution of the given differential equation. Question 12. x 2 dy + (xy + y 2 ) dx = 0; y = 1 when x = 1 Solution : 
Therefore, the given differential equation is a homogeneous equation. To solve it, we make the substitution as: y = vx 
This is the required solution of the given differential equation. Question 13. 
Solution : 
Therefore, the given differential equation is a homogeneous equation. To solve it, we make the substitution as: y = vx 
This is the required solution of the given differential equation. Question 14. 
Solution : 
Therefore, the given differential equation is a homogeneous equation. To solve it, we make the substitution as: y = vx 
This is the required solution of the given differential equation. Question 15. 
Solution : 
Therefore, the given differential equation is a homogeneous equation. To solve it, we make the substitution as: y = vx 
Choose the correct answer: Question 16. A homogeneous differential equation of the form 
can be solved by making the substitution: (A) y = vx (B) v = yx (C) x = vy (D) x = v Solution : We know that a homogeneous differential equation of the form can be solved by the substitution x = vy Therefore, option (C) is correct. Question 17. Which of the following is a homogeneous differential equation: 
Solution : Out of the given four options, option (D) is the only option in which all coefficients of x and y are of same degree i.e., 2. It may be noted that y 2 is a term of second degree. Hence differential equation in option (D) is a Homogeneous differential equation.NCERT Solutions For Class 12 Maths Chapter 9 Exercise 9.5 FAQs
Where can I find NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 online?
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 are available on Physics Wallah.
How can NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 help me in exam preparation?
NCERT Solutions provide step-by-step explanations for each question in the exercise, helping you understand the concepts and problem-solving techniques thoroughly. By practicing these solutions, you can improve your problem-solving skills and prepare effectively for exams.
Can I rely solely on NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 for exam preparation?
While NCERT Solutions are an excellent resource for understanding concepts and practicing problems, it's advisable to supplement them with additional study materials, such as reference books, solved examples, and previous year question papers, to ensure comprehensive exam preparation.
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