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

NCERT solutions for exercise 9.5 Class 12 Maths chapter 9 comes under the topic of homogeneous differential equations. Before going to the sample questions and exercise 9.5 Class 12 Maths, the NCERT Book explains what is a homogeneous equation is and how to identify it. Then a few examples are given and proceed to NCERT solutions for Class 12 Maths chapter 9 exercise 9.5. Questions based on homogeneous differential equations are given in the Class 12 Maths chapter 9 exercise 9.5. Questions to find both particular and general solutions of homogeneous differential equations are present in the Class 12th Maths chapter 6 exercise 9.5. Along with NCERT solutions for Class 12 Maths chapter 9 exercise 9.5 students can practice the following exercises for a better score.

**Also check - **

Differential Equations exercise 9.1

Differential Equations exercise 9.2

Differential Equations exercise 9.3

Differential Equations exercise 9.4

Differential Equations exercise 9.6

Differential Equations miscellaneous exercise

** Differential Equations Class 12 Chapter 9 Exercise: 9.5 **

** Question:1 ** Show that the given differential equation is homogeneous and solve each of them.

** Answer: **

The given diffrential eq can be written as

Let

Now,

Hence, it is a homogeneous equation.

To solve it put ** y = vx Diff ** erentiating on both sides wrt

Substitute this value in equation (i)

Integrating on both side, we get;

Again substitute the value ,we get;

This is the required solution of given diff. equation

** Question:2 ** Show that the given differential equation is homogeneousand solve each of them.

** Answer: **

the above differential eq can be written as,

............................(i)

Now,

Thus the given differential eq is a homogeneous equaion

Now, to solve substitute ** y = vx **** Diff ** erentiating on both sides wrt

Substitute this value in equation (i)

Integrating on both sides, we get; (and substitute the value of )

this is the required solution

** Question:3 ** Show that the given differential equation is homogeneous and solve each of them.

** Answer: **

The given differential eq can be written as;

....................................(i)

Hence it is a homogeneous equation.

Now, to solve substitute ** y = vx **

Differentiating on both sides wrt

Substitute this value in equation (i)

Integrating on both sides, we get;

again substitute the value of

This is the required solution.

** Question:4 ** Show that the given differential equation is homogeneous and solve each of them.

** Answer: **

we can write it as;

...................................(i)

Hence it is a homogeneous equation

Now, to solve substitute ** y = vx **** Diff ** erentiating on both sides wrt

Substitute this value in equation (i)

integrating on both sides, we get

.............[ ]

This is the required solution.

** Question:5 ** Show that the given differential equation is homogeneous and solve it.

** Answer: **

............(i)

Hence it is a homogeneous eq

Now, to solve substitute ** y = vx **** **Differentiating on both sides wrt

Substitute this value in equation (i)

On integrating both sides, we get;

after substituting the value of

This is the required solution

** Question:6 ** Show that the given differential equation is homogeneous and solve it.

** Answer: **

.................................(i)

henxe it is a homogeneous equation

Now, to solve substitute ** y = vx **

Diff erentiating on both sides wrt

Substitute this value in equation (i)

On integrating both sides,

Substitute the value of ** v=y/x , we get **

** Required solution **

** Question:7 ** Solve.

** **

** Answer: **

......................(i)

By looking at the equation we can directly say that it is a homogenous equation.

Now, to solve substitute ** y = vx **

Differentiating on both sides wrt

Substitute this value in equation (i)

integrating on both sides, we get

substitute the value of ** v= y/x , we get **

** Required solution **

** Question:8 ** Solve.

** Answer: **

...............................(i)

it is a homogeneous equation

Now, to solve substitute ** y = vx **

Differentiating on both sides wrt

Substitute this value in equation (i)

On integrating both sides we get;

Required solution

** Question:9 ** Solve.

** Answer: **

..................(i)

hence it is a homogeneous eq

Now, to solve substitute ** y = vx **

Differentiating on both sides wrt

Substitute this value in equation (i)

integrating on both sides, we get; ( ** substituting v =y/x) **

This is the required solution of the given differential eq

** Question:10 ** Solve.

** Answer: **

.......................................(i)

Hence it is a homogeneous equation.

Now, to solve substitute ** x ** ** = yv **

Diff erentiating on both sides wrt

Substitute this value in equation (i)

Integrating on both sides, we get;

This is the required solution of the diff equation.

** Question:11 ** Solve for particular solution.

** Answer: **

..........................(i)

We can clearly say that it is a homogeneous equation.

Now, to solve substitute ** y = vx **

Diff erentiating on both sides wrt

Substitute this value in equation (i)

On integrating both sides

......................(ii)

Now, y=1 and x= 1

After substituting the value of 2k in eq. (ii)

This is the required solution.

** Question:12 ** Solve for particular solution.

** Answer: **

...............................(i)

Hence it is a homogeneous equation

Now, to solve substitute ** y = vx **

Differentiating on both sides wrt

Substitute this value in equation (i), we get

Integrating on both sides, we get;

replace the value of v=y/x

.............................(ii)

Now y =1 and x = 1

therefore,

Required solution

** Question:13 ** Solve for particular solution.

** Answer: **

..................(i)

Hence it is a homogeneous eq

Now, to solve substitute ** y = vx **

Differentiating on both sides wrt

Substitute this value in equation (i)

on integrating both sides, we get;

On substituting ** v =y/x **

............................(ii)

Now,

put this value of C in eq (ii)

Required solution.

** Question:14 ** Solve for particular solution.

** Answer: **

....................................(i)

the above eq is homogeneous. So,

Now, to solve substitute ** y = vx **

Differentiating on both sides wrt

Substitute this value in equation (i)

on integrating both sides, we get;

.................................(ii)

now y = 0 and x =1 , we get

put the value of C in eq 2

** Question:15 ** Solve for particular solution.

** Answer: **

The above eq can be written as;

By looking, we can say that it is a homogeneous equation.

** y = vx **

Differentiating on both sides wrt

Substitute this value in equation (i)

integrating on both sides, we get;

.............................(ii)

Now, y = 2 and x =1, we get

C =-1

put this value in equation(ii)

** Question:16 ** A homogeneous differential equation of the from can be solved by making the substitution.

(A)

(B)

(C)

(D)

** Answer: **

for solving this type of equation put ** x/y = v x = vy **

** option C is correct **

** Question:17 ** Which of the following is a homogeneous differential equation?

(A)

(B)

(C)

(D)

** Answer: **

Option D is the right answer.

we can take out lambda as a common factor and it can be cancelled out

**More About NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5**

To practice the concepts given in topic 9.5.2, 4 example questions are given prior to the exercise 9.5 Class 12 Maths. There are 17 questions in the Class 12 Maths chapter 9 exercise 9.5 and 2 questions of this have 4 choices. As mentioned in the first para certain questions in the Class 12th Maths chapter 6 exercise 9.5 are to find the general solutions and some questions are to find the particular solutions of homogeneous differential equations.

**Also Read| **Differential Equations Class 12th Notes

**Benefits of NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5**

Utilising the exercise 9.5 Class 12 Maths students can master the concepts of identifying the homogeneous equations and finding the solutions to these equations.

Not only for CBSE board exams but also for various state board exams and Engineering Entrance Exams, the NCERT solutions for Class 12 Maths chapter 9 exercise 9.5 can be used.

**Also see-**

NCERT Exemplar Solutions Class 12 Maths Chapter 9

NCERT Solutions for Class 12 Maths Chapter 9

**NCERT Solutions Subject Wise**

NCERT Solutions Class 12 Chemistry

NCERT Solutions for Class 12 Physics

NCERT Solutions for Class 12 Biology

NCERT Solutions for Class 12 Mathematics

**Subject Wise NCERT Exemplar Solutions**

NCERT Exemplar Class 12 Maths

NCERT Exemplar Class 12 Physics

NCERT Exemplar Class 12 Chemistry

NCERT Exemplar Class 12 Biology