NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.5 – CBSE Free PDF Download
Exercise 9.5 of NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations is based on “Homogeneous Differential Equations”. A differential equation is said to be homogeneous if it is a function of the unknown function and its derivatives or if it is written in a particular form, which is explained in detail in the NCERT textbook. Solving the problems given in this exercise helps the students get thorough with the concept of a homogeneous differential equation.
NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations Exercise 9.5
Access Answers to NCERT Class 12 Maths Chapter 9 – Differential Equations Exercise 9.5 Page Number 406
In each of the Exercises 1 to 10, show that the given differential equation is homogeneous and solve each of them.
1. (x2 + x y) dy = (x2 + y2) dx
Solution:
Solution:
3. (x – y) dy – (x + y) dx = 0
Solution:
4. (x2 – y2)dx + 2xy dy = 0
Solution:
On simplification,
x2 + y2 = Cx
Solution:
Solution:
Solution:
Solution:
Solution:
Solution:
For each of the differential equations in Exercises from 11 to 15, find the particular
solution satisfying the given condition.
11. (x + y) dy + (x – y) dx = 0; y = 1 when x = 1
Solution:
12. x2dy + (x y + y2)dx = 0; y = 1 when x = 1
Solution:
Solution:
Solution:
Solution:
The required solution of the differential equation.
16. A homogeneous differential equation of the from 
can be solved by making the substitution.
(A) y = v x (B) v = y x (C) x = v y (D) x = v
Solution:
(C) x = v y
Explanation:
17. Which of the following is a homogeneous differential equation?
A. (4x + 6y + 5) dy – (3y + 2x + 4) dx = 0
B. (x y) dx – (x3 + y3) dy = 0
C. (x3 + 2y2) dx + 2xy dy = 0
D. y2dx + (x2 – x y – y2) dy = 0
Solution:
D. y2dx + (x2 – x y – y2) dy = 0
Explanation:
Access Other Exercise Solutions of Class 12 Maths Chapter 9
Exercise 9.1 Solutions 12 Questions
Exercise 9.2 Solutions 12 Questions
Exercise 9.3 Solutions 12 Questions
Exercise 9.4 Solutions 23 Questions
Exercise 9.6 Solutions 19 Questions
Miscellaneous Exercise on Chapter 9 Solutions 18 Questions
Also, explore –
Comments