NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations Exercise 9.5

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Exercise 9.5 – CBSE Term II 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.

Download PDF of NCERT Solutions for Class 12 Maths Chapter 9 – Differential Equations Exercise 9.5

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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:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 116

NCERT Solutions for Class 12 Maths Chapter 9 - Image 117

NCERT Solutions for Class 12 Maths Chapter 9 - Image 119

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 120

NCERT Solutions for Class 12 Maths Chapter 9 - Image 121

NCERT Solutions for Class 12 Maths Chapter 9 - Image 122

3. (x – y) dy – (x + y) dx = 0

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 123

NCERT Solutions for Class 12 Maths Chapter 9 - Image 124

NCERT Solutions for Class 12 Maths Chapter 9 - Image 125

NCERT Solutions for Class 12 Maths Chapter 9 - Image 126

4. (x2 – y2)dx + 2xy dy = 0

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 127

NCERT Solutions for Class 12 Maths Chapter 9 - Image 128

NCERT Solutions for Class 12 Maths Chapter 9 - Image 129

NCERT Solutions for Class 12 Maths Chapter 9 - Image 130

On simplification

x2 + y2 = Cx

NCERT Solutions for Class 12 Maths Chapter 9 - Image 131

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 132

NCERT Solutions for Class 12 Maths Chapter 9 - Image 133

NCERT Solutions for Class 12 Maths Chapter 9 - Image 134

NCERT Solutions for Class 12 Maths Chapter 9 - Image 135

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 136

NCERT Solutions for Class 12 Maths Chapter 9 - Image 137

NCERT Solutions for Class 12 Maths Chapter 9 - Image 138

NCERT Solutions for Class 12 Maths Chapter 9 - Image 139

NCERT Solutions for Class 12 Maths Chapter 9 - Image 140

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 141

NCERT Solutions for Class 12 Maths Chapter 9 - Image 142

NCERT Solutions for Class 12 Maths Chapter 9 - Image 143

NCERT Solutions for Class 12 Maths Chapter 9 - Image 144

NCERT Solutions for Class 12 Maths Chapter 9 - Image 145

NCERT Solutions for Class 12 Maths Chapter 9 - Image 146

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 147

NCERT Solutions for Class 12 Maths Chapter 9 - Image 148

NCERT Solutions for Class 12 Maths Chapter 9 - Image 149

NCERT Solutions for Class 12 Maths Chapter 9 - Image 150

NCERT Solutions for Class 12 Maths Chapter 9 - Image 151

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 152

NCERT Solutions for Class 12 Maths Chapter 9 - Image 153

NCERT Solutions for Class 12 Maths Chapter 9 - Image 154

NCERT Solutions for Class 12 Maths Chapter 9 - Image 155

NCERT Solutions for Class 12 Maths Chapter 9 - Image 156

NCERT Solutions for Class 12 Maths Chapter 9 - Image 157

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 158

NCERT Solutions for Class 12 Maths Chapter 9 - Image 159

NCERT Solutions for Class 12 Maths Chapter 9 - Image 160

NCERT Solutions for Class 12 Maths Chapter 9 - Image 161

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:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 162

NCERT Solutions for Class 12 Maths Chapter 9 - Image 163

NCERT Solutions for Class 12 Maths Chapter 9 - Image 164

NCERT Solutions for Class 12 Maths Chapter 9 - Image 165

NCERT Solutions for Class 12 Maths Chapter 9 - Image 166

12. x2dy + (x y + y2)dx = 0; y = 1 when x = 1

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 167

NCERT Solutions for Class 12 Maths Chapter 9 - Image 168

NCERT Solutions for Class 12 Maths Chapter 9 - Image 169

NCERT Solutions for Class 12 Maths Chapter 9 - Image 170

NCERT Solutions for Class 12 Maths Chapter 9 - Image 171

NCERT Solutions for Class 12 Maths Chapter 9 - Image 172

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 173

NCERT Solutions for Class 12 Maths Chapter 9 - Image 174

NCERT Solutions for Class 12 Maths Chapter 9 - Image 175

NCERT Solutions for Class 12 Maths Chapter 9 - Image 176

NCERT Solutions for Class 12 Maths Chapter 9 - Image 177

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 178

NCERT Solutions for Class 12 Maths Chapter 9 - Image 179

NCERT Solutions for Class 12 Maths Chapter 9 - Image 180

NCERT Solutions for Class 12 Maths Chapter 9 - Image 181

Solution:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 182

NCERT Solutions for Class 12 Maths Chapter 9 - Image 183

NCERT Solutions for Class 12 Maths Chapter 9 - Image 184

The required solution of the differential equation.

16. A homogeneous differential equation of the from NCERT Solutions for Class 12 Maths Chapter 9 - Image 185can 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:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 186

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:

NCERT Solutions for Class 12 Maths Chapter 9 - Image 187

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

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