NCERT Solution Class 12 Chapter 9- Differential Equations Exercise 9.4

The Exercise 9.4 of NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations is based on solving first order, first degree differential equations with variables separable. One of the easiest kinds of differential equation to solve is a first order equation with separable variables. “First order” means that the highest derivative appearing in the equation is the first. “Separable variables” means the equation is in the form, or can be placed in the form, dy/dx = f(x)g(y).Get thorough with the topic of differential equations with variable separable by solving the questions present in this exercise.

Download PDF of NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations Exercise 9.4

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Access Answers of Maths NCERT Class 12 Maths Chapter 9- Differential Equations Exercise 9.4 Page Number 395

For each of the differential equations in Exercises 1 to 10, find the general solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 57

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 58

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 59

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 60

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 61

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 62

Solution:

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NCERT Solutions for Class 12 Maths Chapter 9 -  Image 64

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 65

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 66

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 67

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 68

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 69

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 70

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 71

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 72

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 73

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 74

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 75

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 76

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 77

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 78

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 79

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 80

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 81

For each of the differential equations in Exercises 11 to 14, find a particular solution

Satisfying the given condition:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 82

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 83

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 84

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 85

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 86

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 87

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 88

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 89

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 90

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 91

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 92

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 93

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 94

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 95

⇒ c = 1

Putting the value of c in 1

⇒ y = sec x

15. Find the equation of a curve passing through the point (0, 0) and whose differential equation is y′ = ex sin x

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 96

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 97

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 98

Find the solution curve passing through the point (1, –1).

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 99

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 100

17. Find the equation of a curve passing through the point (0, –2) given that at any

point (x, y) on the curve, the product of the slope of its tangent and y coordinate

of the point is equal to the x coordinate of the point.

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 101

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 102

18. At any point (x, y) of a curve, the slope of the tangent is twice the slope of the

line segment joining the point of contact to the point (– 4, –3). Find the equation

of the curve given that it passes through (–2, 1).

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 103

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 104

19. The volume of spherical balloon being inflated changes at a constant rate. If

initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of

balloon after t seconds.

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 105

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 106

20. In a bank, principal increases continuously at the rate of r% per year. Find the

value of r if Rs 100 double itself in 10 years (loge 2 = 0.6931).

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 107

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 108

21. In a bank, principal increases continuously at the rate of 5% per year. An amount

of Rs 1000 is deposited with this bank, how much will it worth after 10 years

(e0.5 = 1.648).

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 109

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 110

22. In a culture, the bacteria count is 1, 00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2, 00,000, if the rate of growth of bacteria is proportional to the number present?

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 111

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 112

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 113

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 114

Solution:

(A) ex + e-y = C

Explanation:

NCERT Solutions for Class 12 Maths Chapter 9 -  Image 115

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 9.5 Solutions 17 Questions

Exercise 9.6 Solutions 19 Questions

Miscellaneous Exercise On Chapter 9 Solutions 18 Questions

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