NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.6 (Differential Equations)
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.6 contains all the questions with detailed solutions. Students are advised to solve these questions for better understanding of the concepts in exercise 9.6.
Krati Saraswat10 Feb, 2024
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NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.6 (Differential Equations)
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.6 Differential Equations is prepared by the academic team of Physics Wallah. We have prepared NCERT Solutions for all exercise of Chapter 9. Below are step-by-step solutions to all questions given in the NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.6 Differential Equations.NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.6 Overview
NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.6 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 results.NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.6
Solve The Following Questions of NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.6:
In each of the following differential equations given in each Questions 1 to 4, find the general solution: Question 1.
Solution :
Given: Differential equation
This is the required general solution of the given differential equation.
Question
2.
Solution :
Question
3.
Solution :
Given: Differential equation
Question
4.
Solution :
Given: Differential equation
For each of the following differential equations given in Question 5 to 8, find the general solution:
Question
5.
Solution :
The given differential equation is:
Question
6.
Solution :
Given: Differential equation
Question
7.
Solution :
Given: Differential equation
Question
8.
Solution :
Given: Differential equation
For each of the following differential equations given in Question 9 to 12, find the general solution:
Question
9.
Solution :
Given: Differential equation
Question
10.
Solution :
Given: Differential equation
Question
11.
Solution :
Given: Differential equation
Question
12.
Solution :
Given: Differential equation
For each of the differential equations given in Questions 13 to 15, find a particular solution satisfying the given condition:
Question
13.
Solution :
Given: Differential equation
This is a linear equation of the form:
Hence, the required solution of the given differential equation is y = cos x - 2 cos
2
x.
Question
14.
Solution :
Given: Differential equation
This is the required general solution of the given differential equation.
Question
15.
Solution :
Given: Differential equation
This is the required particular solution of the given differential equation.
Question
16. Find the equation of the curve passing through the origin, given that the slope of the tangent to the curve at any point (
x
,
y
) is equal to the sum of coordinates of that point.
Solution :
Let
F
(
x
,
y
) be the curve passing through the origin.
At point (
x
,
y
), the slope of the curve will be dy/dx.
According to the given information:
The curve passes through the origin.
Therefore, equation (2) becomes:
1 = C
⇒ C = 1
Substituting C = 1 in equation (2), we get:
x + y + 1 = e
x
Hence, the required equation of curve passing through the origin is x + y + 1 = e
x
.
Question
17. Find the equation of the curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangents to the curve at that point by 5.
Solution :
Let
F
(
x
,
y
) be the curve and let (
x
,
y
) be a point on the curve. The slope of the tangent to the curve at (
x
,
y
) is dy/dx.
According to the given information:
The curve passes through point (0, 2).
Therefore, equation (2) becomes:
0 + 2 – 4 = C
e
0
⇒ – 2 = C
⇒ C = – 2
Substituting C = –2 in equation (2), we get:
x + y -4 = - 2e
x
⇒y = 4 - x - 2e
x
This is the required equation of the curve.
Question
18. Choose the correct answer:
The integrating factor of the differential equation is:
(A)
e
–
x
(B)
e
–
y
(C) 1/x
(D)
x
Solution :
Given: Differential equation
Therefore, option (C) is correct.
Question
19. Choose the correct answer:
The integrating factor of the differential equation
Solution :
Given: Differential equation
Therefore, option (D) is correct.
NCERT Solutions For Class 12 Maths Chapter 9 Exercise 9.6 FAQs
What is most important in class 9 maths?
The highest scoring chapter is Polynomials. If you want to clear your exam with flying results, you need to prepare this chapter well. Practice as many questions as you can, calculation mistakes are a major factor in this chapter.
Who is the father of mathematics?
Archimedes is widely regarded as one of the greatest mathematicians in history, earning him the title of the "Father of Mathematics."
Will I pass 9th if I fail in one subject?
If a student fails in one subject in class 9 CBSE, they will not be promoted to class 10 and will have to repeat class 9.
What is a differential equation first?
A first-order differential equation is generally of the form F(x, y, y') = 0, where y is a dependent variable and x is an independent variable and y' appears explicitly in the differential equation.
What are the disadvantages of differential equations?
The disadvantage of a differential equation is that it may not have solutions that you can express in terms of elementary functions, and it requires substantial mathematical machinery to understand them at any depth.
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