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Most class 12 students use the RD Sharma Solution books to clarify their doubts while doing homework. However, when it comes to mathematics, the students feel nervous about solving the sums in new concepts. Chapters like the Differential Equations are challenging for most of the students. The arrival of RD Sharma Class 12th Chapter 21 FBQ solution books has helped many students of this category.

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Differential Equation exercise Fill in the blank question 1

Answer:

1

Hint:

Since, Parabola has symmetric along positive x-axis, its equation is y^{2 }= 4ax

Number of arbitrary constants = Order of differential Equation

Given:

The order of differential equation representing the family of parabola y^{2} = 4ax is _____

Solution:

We know that order of differential equation = no. of arbitrary constant. Here, no. of arbitrary constant is 1

So, 1 is the arbitrary constant.

∴ The answer is 1.

1

Hint:

Since, Parabola has symmetric along positive x-axis, its equation is y

Number of arbitrary constants = Order of differential Equation

Given:

The order of differential equation representing the family of parabola y

Solution:

We know that order of differential equation = no. of arbitrary constant. Here, no. of arbitrary constant is 1

So, 1 is the arbitrary constant.

∴ The answer is 1.

Differential Equation exercise Fill in the blank question 2

Answer:

2

Hint:

The degree of the differential equation is the power of highest order derivative present in the differential equation.

Given:

Solution:

The order of the given equation

Degree is the power of the highest order derivative.

So, the degree in this equation is 2.

∴The answer is 2

2

Hint:

The degree of the differential equation is the power of highest order derivative present in the differential equation.

Given:

Solution:

The order of the given equation

Degree is the power of the highest order derivative.

So, the degree in this equation is 2.

∴The answer is 2

Differential Equation exercise Fill in the blank question 3

Answer:

0

Hint:

In particular solution Number of arbitrary constant = 0.

Given:

The number of arbitrary constants in a particular solution of the differential equation tanx dx + tany dy=0

Solution:

Tanx dx + tany dy=0, any particular solution of a differential equation has no arbitrary constant.

So, the answer is 0(zero).

0

Hint:

In particular solution Number of arbitrary constant = 0.

Given:

The number of arbitrary constants in a particular solution of the differential equation tanx dx + tany dy=0

Solution:

Tanx dx + tany dy=0, any particular solution of a differential equation has no arbitrary constant.

So, the answer is 0(zero).

Differential Equation exercise Fill in the blank question 4

Answer:

x = v y

Hint:

Substituting the equation

Given:

Solution:

As there are x/y present in equation 3 times. So, it is good to use replacement x=v y.

It will simplify the equation to solve it easily.

∴ The answer is x=v y

x = v y

Hint:

Substituting the equation

Given:

Solution:

As there are x/y present in equation 3 times. So, it is good to use replacement x=v y.

It will simplify the equation to solve it easily.

∴ The answer is x=v y

Differential Equation exercise Fill in the blank question 5

Answer:

Hint:

We will use the method of solving linear differential equation.

Given:

Solution:

The given differential equation can be written as

The given differential equation is of the form

and therefore by comparison we get;

So, the answer is

Hint:

We will use the method of solving linear differential equation.

Given:

Solution:

The given differential equation can be written as

The given differential equation is of the form

and therefore by comparison we get;

So, the answer is

Differential Equation exercise Fill in the blank question 6

Answer:

Hint:

First use the variable separation method then integrating both sides.

Given:

Solution:

So, the answer is

Hint:

First use the variable separation method then integrating both sides.

Given:

Solution:

So, the answer is

Differential Equation exercise Fill in the blank question 7

Answer:

Hint:

Using the form

Given:

Solution:

Comparing with the given equation with

We get,

∴The general solution is

So the answer is

Hint:

Using the form

Given:

Solution:

Comparing with the given equation with

We get,

∴The general solution is

So the answer is

Differential Equation exercise Fill in the blank question 8

Answer:

Hint:

Differentiating the given function w.r.t ‘x’

Given:

Solution:

Differentiating the given function w.r.t ‘x’ we get,

and

is the required differential equation.

∴So, the answer is

Hint:

Differentiating the given function w.r.t ‘x’

Given:

Solution:

Differentiating the given function w.r.t ‘x’ we get,

and

is the required differential equation.

∴So, the answer is

Differential Equation exercise Fill in the blank question 9

Answer:

Hint:

Use the concept of linear Differential equation is of the form

Given:

Solution:

The equation in the form

Where

So, the answer is

Hint:

Use the concept of linear Differential equation is of the form

Given:

Solution:

The equation in the form

Where

So, the answer is

Differential Equation exercise Fill in the blank question 10

Answer:

2

Hint:

Differentiating w.r.t to ‘x’

Given:

The family of ellipses having foci on x-axis and center at the origin, is given by

Solution:

Differentiating w.r.t ‘x’, we get

Again by differentiating w.r.t ‘x’ we get

The required equation is

∴ Order of the differential equation is the highest derivative present in the differential equation(i)

So, the answer is 2

2

Hint:

Differentiating w.r.t to ‘x’

Given:

The family of ellipses having foci on x-axis and center at the origin, is given by

Solution:

Differentiating w.r.t ‘x’, we get

Again by differentiating w.r.t ‘x’ we get

The required equation is

∴ Order of the differential equation is the highest derivative present in the differential equation(i)

So, the answer is 2

Differential Equation exercise Fill in the blank question 11

Answer:

1

Hint:

Squaring both sides

Given:

Solution:

On squaring the given differential equation,

Highest order of the given equation is

and degree of

∴ Degree of the differential equation is 1.

∴So, the answer is 1.

1

Hint:

Squaring both sides

Given:

Solution:

On squaring the given differential equation,

Highest order of the given equation is

and degree of

∴ Degree of the differential equation is 1.

∴So, the answer is 1.

Differential Equation exercise Fill in the blank question 12

Answer:

Hint:

Using the form of linear differential equation

Given:

Solution:

Divide the eqn (i) by x, we get

Comparing eqn (ii) with the standard linear differential equation

We get,

∴So the answer is

Hint:

Using the form of linear differential equation

Given:

Solution:

Divide the eqn (i) by x, we get

Comparing eqn (ii) with the standard linear differential equation

We get,

∴So the answer is

Differential Equation exercise Fill in the blank question 13

Answer:

Not defined

Hint:

We cannot express polynomial of derivatives

Given:

Solution:

Degree of this equation is not defined as it cannot be expressed as polynomial of derivatives.

So, the answer is not defined.

Not defined

Hint:

We cannot express polynomial of derivatives

Given:

Solution:

Degree of this equation is not defined as it cannot be expressed as polynomial of derivatives.

So, the answer is not defined.

Differential Equation exercise Fill in the blank question 14

Answer:

2

Hint:

Degree is the highest exponent of the highest order derivative.

Given:

Solution:

The degree is the highest exponent of the highest order derivative and it is 2 in this equation.

So, the answer is 2

2

Hint:

Degree is the highest exponent of the highest order derivative.

Given:

Solution:

The degree is the highest exponent of the highest order derivative and it is 2 in this equation.

So, the answer is 2

Differential Equation exercise Fill in the blank question 15

Answer:

3

Hint:

Number of arbitrary constants = Order of differential Equation

Given:

The number of arbitrary constants in the general solution of the differential equation of order 3 is_____.

Solution:

As per the given question the numbers of arbitrary constants in third order differential equation are 3.

So the answer is 3.

3

Hint:

Number of arbitrary constants = Order of differential Equation

Given:

The number of arbitrary constants in the general solution of the differential equation of order 3 is_____.

Solution:

As per the given question the numbers of arbitrary constants in third order differential equation are 3.

So the answer is 3.

Differential Equation exercise Fill in the blank question 16

Answer:

Hint:

Using the form

Given:

where R and S are functions of y.

Solution:

Integrating factor of given differential equation is

General solution is given by:

So, the answer is

Hint:

Using the form

Given:

where R and S are functions of y.

Solution:

Integrating factor of given differential equation is

General solution is given by:

So, the answer is

Differential Equation exercise Fill in the blank question 17

Answer:

Hint:

Use the form

to find the integrating factor.

Given:

Solution:

Where

So, the answer is

Hint:

Use the form

to find the integrating factor.

Given:

Solution:

Where

So, the answer is

Differential Equation exercise Fill in the blank question 18

Answer:

Hint:

Integrating both sides

Given:

Solution:

Separate the variable and integrating both sides, we get

So, the answer is C sec y

Hint:

Integrating both sides

Given:

Solution:

Separate the variable and integrating both sides, we get

So, the answer is C sec y

Differential Equation exercise Fill in the blank question 19

Answer:

Hint:

Substituting the values

Given:

Solution:

On dividing the given differential equation by x, we get

So, the differential equation is a linear differential equation, and we can observe that the given differential equation is in the form

where,

Here we get the integrating factor as

By substituting the values,

We get,

Here, the general solution can be written as

Substituting the values we get

Dividing the entire equation by x^{2}

So, the answer is

Hint:

Substituting the values

Given:

Solution:

On dividing the given differential equation by x, we get

So, the differential equation is a linear differential equation, and we can observe that the given differential equation is in the form

where,

Here we get the integrating factor as

By substituting the values,

We get,

Here, the general solution can be written as

Substituting the values we get

Dividing the entire equation by x

So, the answer is

Differential Equation exercise Fill in the blank question 20

Answer:

Hint:

First separate the variables and then use simple Integrating to solve the question.

Given:

Solution:

Hence, the answer is

Hint:

First separate the variables and then use simple Integrating to solve the question.

Given:

Solution:

Hence, the answer is

Differential Equation exercise Fill in the blank question 21

Answer:

Order = 1

Given:

The order of differential equation representing the family of circles

x^{2} + (y-a)^{2 }=a^{2 }Is _________

Hint:

Order = No. of arbitrary constant

Solution:

We know that, order of differential equation = no. of arbitrary constant. Here, no. of arbitrary constant is 1

∴So, the answer is 1

Order = 1

Given:

The order of differential equation representing the family of circles

x

Hint:

Order = No. of arbitrary constant

Solution:

We know that, order of differential equation = no. of arbitrary constant. Here, no. of arbitrary constant is 1

∴So, the answer is 1

Differential Equation exercise Fill in the blank question 22

Answer:

Order =0

Given:

The number of arbitrary constants in the particular solution of a differential equation of order two is ________

Hint:

Here, number of arbitrary constant = order of the equation

Solution:

Particular solution of a differential equation doesn’t contain any arbitrary constant.

So, the number of arbitrary constant in the particular solution of a differential equation = 0

So the answer is ‘0’

Order =0

Given:

The number of arbitrary constants in the particular solution of a differential equation of order two is ________

Hint:

Here, number of arbitrary constant = order of the equation

Solution:

Particular solution of a differential equation doesn’t contain any arbitrary constant.

So, the number of arbitrary constant in the particular solution of a differential equation = 0

So the answer is ‘0’

Differential Equation exercise Fill in the blank question 23

Answer:

Given:

The differential equation of all non-horizontal lines in a plane is ____

Hint:

Solution:

Equation of non-horizontal line in a plane is y = mx + c where ‘m’ is slope.

Since, there are two arbitrary constants. so the order will be two hence we can differentiate the equation of line two times.

Differentiate w.r.t x

So, the answer is

Given:

The differential equation of all non-horizontal lines in a plane is ____

Hint:

Solution:

Equation of non-horizontal line in a plane is y = mx + c where ‘m’ is slope.

Since, there are two arbitrary constants. so the order will be two hence we can differentiate the equation of line two times.

Differentiate w.r.t x

So, the answer is

Differential Equation exercise Fill in the blank question 24

Answer:

Given:

The differential equation of all non-vertical lines in a plane is ____

Hint:

Solution:

Clearly, equation of all non-vertical lines is y=mx+c

On differentiating w.r.t x we get

and differentiating again We get:

So, the answer is

Given:

The differential equation of all non-vertical lines in a plane is ____

Hint:

Solution:

Clearly, equation of all non-vertical lines is y=mx+c

On differentiating w.r.t x we get

and differentiating again We get:

So, the answer is

Differential Equation exercise Fill in the blank question 25

Answer:Integrating factor = x

Hint:

we will use the linear differential equation to solve the problem.

Given:

The integrating factor of all differential equation

is _________

Dividing the given equation both sides by x

Solution:

Dividing the L.H.S by (x

Clearly, the equation (i) is of the form

Comparing (i) and (ii) we get,

So,

Now Put x

So, the answer is x

Differential Equation exercise Fill in the blank question 26

Answer:

Degree=4

Hint:

Degree = Highest power of the highest order derivative.

Given:

The degree of differential equation

is _______

Solution:

So, the degree of above differential equation is 4

Degree=4

Hint:

Degree = Highest power of the highest order derivative.

Given:

The degree of differential equation

is _______

Solution:

So, the degree of above differential equation is 4

Differential Equation exercise Fill in the blank question 27

Answer:

Order = 2 or 2^{nd} order

Given:

The order of differential equation representing all circles of radius r is ____

Hint:

Here, Order = Highest derivative

Solution:

Any circle with given radius can be written as (x-h)^{2}+(y-k)^{2}=r^{2}

Where (h, k) be the Centre of the circle and radius is constant.

Differentiating both side w.r.t x we get

Hence order of differential equation will be ‘2’ i.e. 2^{nd} order.

So, the answer is ‘2’ or 2^{nd} order.

Order = 2 or 2

Given:

The order of differential equation representing all circles of radius r is ____

Hint:

Here, Order = Highest derivative

Solution:

Any circle with given radius can be written as (x-h)

Where (h, k) be the Centre of the circle and radius is constant.

Differentiating both side w.r.t x we get

Hence order of differential equation will be ‘2’ i.e. 2

So, the answer is ‘2’ or 2

Differential Equation exercise Fill in the blank question 28

Answer:

Degree = 3

Hint:

To find the degree of differential equation representing the family of curves y = Ax + A^{3},we have to eliminate the constant A.

Given:

The degree of differential equation representing the family of curves y = Ax + A^{3}, where A is arbitrary constant is ______

Solution:

Using the eqn (ii) in (i), we get

Hence, Degree = Highest power of the highest order derivative.

So, the degree of the above differential equation is 3.

Degree = 3

Hint:

To find the degree of differential equation representing the family of curves y = Ax + A

Given:

The degree of differential equation representing the family of curves y = Ax + A

Solution:

Using the eqn (ii) in (i), we get

Hence, Degree = Highest power of the highest order derivative.

So, the degree of the above differential equation is 3.

Differential Equation exercise Fill in the blank question 29

Answer:

xy = C

Given:

The general solution of the differential equation

is _____

Hint:

The above sum will be solved by the formula of derivatives.

Solution:

So, the answer is xy = C

xy = C

Given:

The general solution of the differential equation

is _____

Hint:

The above sum will be solved by the formula of derivatives.

Solution:

So, the answer is xy = C

Differential Equation exercise Fill in the blank question 30

Answer:

Order=3 and Degree=1

Given:

The order and degree of the differential equation

are ____ and ____ respectively.

Hint:

Order = Highest Derivative

Degree = Highest power of highest order Derivative

Solution:

Order = Highest Derivative = 3

Degree = Highest power of highest Derivative = 1

So, the order is 3 and degree is 1.

Order=3 and Degree=1

Given:

The order and degree of the differential equation

are ____ and ____ respectively.

Hint:

Order = Highest Derivative

Degree = Highest power of highest order Derivative

Solution:

Order = Highest Derivative = 3

Degree = Highest power of highest Derivative = 1

So, the order is 3 and degree is 1.

Differential Equation exercise Fill in the blank question 31

Answer:

Hint:

Use simple differentiation w.r.t x

Given:

The differential equation for which y=a cos x + b sin x is a solution, is ____

Solution:

differentiating both side w.r.t x, we get

Again differentiating both side w.r.t x, we get

Now, we have to verify

Taking L.H.S

∴So, the differential equation is

Hint:

Use simple differentiation w.r.t x

Given:

The differential equation for which y=a cos x + b sin x is a solution, is ____

Solution:

differentiating both side w.r.t x, we get

Again differentiating both side w.r.t x, we get

Now, we have to verify

Taking L.H.S

∴So, the differential equation is

Differential Equation exercise Fill in the blank question 32

Answer:

Rectangular Hyperbola

Hint:

Ratio of abscissa and ordinate = rectangular hyperbola

Given:

The curve for which the slope of the tangent at any point is equal to the ratio of abscissa and ordinate of the point is ______

Solution:

The curve for which the slope of the tangent at any point is equal to the ratio of abscissa and ordinate of the point is ‘Rectangular Hyperbola’

So the answer is Rectangular Hyperbola.

Rectangular Hyperbola

Hint:

Ratio of abscissa and ordinate = rectangular hyperbola

Given:

The curve for which the slope of the tangent at any point is equal to the ratio of abscissa and ordinate of the point is ______

Solution:

The curve for which the slope of the tangent at any point is equal to the ratio of abscissa and ordinate of the point is ‘Rectangular Hyperbola’

So the answer is Rectangular Hyperbola.

Differential Equation exercise Fill in the blank question 33

Answer:

Order=1 and Degree=3

Given:

Family y = Ax + A^{3} of curves will correspond to a differential equation of order and degree _____

Hint:

Order=Highest Derivative

Solution:

Given, family of curves is

Putting the value of A in equation (i)

∴ Order = 1

∴ Degree= Highest power of Derivative=3

∴So, the order is 1 and degree is 3

Order=1 and Degree=3

Given:

Family y = Ax + A

Hint:

Order=Highest Derivative

Solution:

Given, family of curves is

Putting the value of A in equation (i)

∴ Order = 1

∴ Degree= Highest power of Derivative=3

∴So, the order is 1 and degree is 3

Differential Equation exercise Fill in the blank question 34

Answer:

Hyperbola

Given:

The differential equation xdy + ydx = 0 represents the family of ____

Hint:

By the help of integral sums will get solve.

Solution:

Integrating both sides

So, the above differential equation represents the Hyperbola.

Hyperbola

Given:

The differential equation xdy + ydx = 0 represents the family of ____

Hint:

By the help of integral sums will get solve.

Solution:

Integrating both sides

So, the above differential equation represents the Hyperbola.

Differential Equation exercise Fill in the blank question 35

Answer:

Hint:

To remove the arbitrary constant we have differentiate the given equation.

Given:

The differential equation of the family of curves x^{2} + y^{2} - 2ay = 0, where a is arbitrary constant is _____

Solution:

So, the answer is

Hint:

To remove the arbitrary constant we have differentiate the given equation.

Given:

The differential equation of the family of curves x

Solution:

So, the answer is

Differential Equation exercise Fill in the blank question 36

Answer:

Order = 2, Degree = 1

Hint:

Order=Highest Derivative

Degree=Highest power of highest Derivative

Given:

The order and degree of the differential equation

are ____respectively.

Solution:

By using chain we will evaluate the derivative

∴Order = Highest Derivative i.e. 2

∴ Degree = The highest power the highest derivative is 1

So the order and degree are 2,1 respectively.

Order = 2, Degree = 1

Hint:

Order=Highest Derivative

Degree=Highest power of highest Derivative

Given:

The order and degree of the differential equation

are ____respectively.

Solution:

By using chain we will evaluate the derivative

∴Order = Highest Derivative i.e. 2

∴ Degree = The highest power the highest derivative is 1

So the order and degree are 2,1 respectively.

Differential Equation exercise Fill in the blank question 37

Answer:

Given:

The integrating factor of differential equation

is ______

Hint:

By the help of integrating factor the sum will solve.

Solution:

Comparing the above equation with the standard linear differential equation, we get

Here,

So, integrating factor

So, the answer is

Given:

The integrating factor of differential equation

is ______

Hint:

By the help of integrating factor the sum will solve.

Solution:

Comparing the above equation with the standard linear differential equation, we get

Here,

So, integrating factor

So, the answer is

Class 12, chapter 21, Differential Equations, consists of eleven exercises, ex 21.1 to ex 21.11. every exercise revolves around the same concept of differentiation in various methods. The Fill in the Blank Questions (FBQ) section consists of 55 questions asked from various exercises given in the textbook. The concepts in this portion revolve around solving a differential equation, formation of a differential equation, integrating factors of the differential equation, and so on. The RD Sharma Class 12 Chapter 21 FBQ book helps the students in finding the right way to find the answers to those questions.

The RD Sharma books can be referred to while doing homework, assignments, preparing for class tests, public exams, and even JEE mains exams. It covers the NCERT syllabus, which makes the CBSE board schools’ students adapt easily. The RD Sharma Class 12th Chapter 21 FBQ solution guide consists of various other practice questions to make the students well-versed in the objectives part. The more questions students practice before their exams, the more confidence they would gain to face challenging questions. This eventually makes them score more than their benchmark easily.

Every answer provided in the Class 12 RD Sharma Chapter 21 FBQ Solution book is framed by mathematical experts. Differential integrations will no longer be tricky for students who have good practice using the RD Sharma Class 12 Solutions Differential Equation Chapter 21 FBQ book. The students would become familiar with the sums effortlessly. By practicing with the same bok for their homework, assignments and exam preparation, they will develop good practice in less time.

The primary advantage that makes the RD Sharma Class 12th Chapter 21 FBQ followed by many students is that this set of books is available for free of cost at the Career 360 website. Why would anyone wish to spend hundreds and thousands of rupees for a solution book when the RD Sharma Class 12 Solutions Chapter 21 FBQ book is available for free? So now, it is your turn to own a copy of these best reference materials to enhance your knowledge and increase your scores.1. What is the most recommended solution book by the previous batch class 12 students?

Most of the previous batch class 12 students recommend the RD Sharma Class 12th Chapter 21 FBQ solution book to their juniors. This is due to the clarity of sums present in these guides, which are helpful for the students.

2. What is the resource to obtain the RD Sharma Solution books for free of cost?

The RD Sharma reference guides can be obtained from the Career 360 website without paying even a penny.

3. How many Fill in the Blank (FBQ) questions does the RD Sharma chapter 21 book cover?

The RD Sharma Class 12th Chapter 21 FBQ reference book consists of answers for all the 55 questions given in the textbook, along with various additional practice questions.

4. Can the CBSE Students use the RD Sharma solution guides to clarify their doubts?

The CBSE school students predominantly use the RD Sharma solution books based on the NCERT pattern. Therefore, no student needs to hesitate to own a copy of these books.

5. How much does it cost to access the RD Sharma books at the Career 360 website?

To view or download the RD Sharma solution books, no money is charged. It is free to own a copy of the best reference guides.

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