NCERT Solution Class 12 Chapter 9- Differential Equations Exercise 9.5

The 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 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 of Maths 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 118

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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