NCERT Solutions for Class 12 Maths Maths Part-2 Chapter 9

Differential Equations Class 12

Chapter 9 Differential Equations Exercise 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, miscellaneous Solutions

<< Previous Chapter 8 : Application of Integrals Next Chapter 10 : Vector Algebra >>

Exercise 9.1 : Solutions of Questions on Page Number : 382

Q1 :  

Determine order and degree(if defined) of differential equation


Answer :

The highest order derivative present in the differential equation is. Therefore, its order is four.

The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.

Answer needs Correction? Click Here

Q2 :  

Determine order and degree(if defined) of differential equation


Answer :

The given differential equation is:

The highest order derivative present in the differential equation is. Therefore, its order is one.

It is a polynomial equation in. The highest power raised tois 1. Hence, its degree is one.

Answer needs Correction? Click Here

Q3 :  

Determine order and degree(if defined) of differential equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Determine order and degree(if defined) of differential equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Determine order and degree(if defined) of differential equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Determine order and degree(if defined) of differential equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Determine order and degree(if defined) of differential equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

Determine order and degree(if defined) of differential equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Determine order and degree(if defined) of differential equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Determine order and degree(if defined) of differential equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

The degree of the differential equation

is

(A) 3 (B) 2 (C) 1 (D) not defined


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

The order of the differential equation

is

(A) 2 (B) 1 (C) 0 (D) not defined


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 8 : Application of Integrals Next Chapter 10 : Vector Algebra >>

Exercise 9.2 : Solutions of Questions on Page Number : 385

Q1 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

The numbers of arbitrary constants in the general solution of a differential equation of fourth order are:

(A) 0 (B) 2 (C) 3 (D) 4


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

The numbers of arbitrary constants in the particular solution of a differential equation of third order are:

(A) 3 (B) 2 (C) 1 (D) 0


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 8 : Application of Integrals Next Chapter 10 : Vector Algebra >>

Exercise 9.3 : Solutions of Questions on Page Number : 391

Q1 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Form the differential equation of the family of circles touching the y-axis at the origin.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Form the differential equation of the family of hyperbolas having foci on x-axis and centre at origin.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Form the differential equation of the family of circles having centre on y-axis and radius 3 units.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

Which of the following differential equations hasas the general solution?

A.

B.

C.

D.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

Which of the following differential equation hasas one of its particular solution?

A.

B.

C.

D.


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 8 : Application of Integrals Next Chapter 10 : Vector Algebra >>

Exercise 9.4 : Solutions of Questions on Page Number : 395

Q1 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

Find the equation of a curve passing through the point (0, 0) and whose differential equation is.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

For the differential equation find the solution curve passing through the point (1, –1).


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

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


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q18 :  

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).


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q19 :  

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.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q20 :  

In a bank, principal increases continuously at the rate of r% per year. Find the value of r if Rs 100 doubles itself in 10 years (log­e 2 = 0.6931).


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q21 :  

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.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q22 :  

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?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q23 :  

The general solution of the differential equation

A.

B.

C.

D.


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 8 : Application of Integrals Next Chapter 10 : Vector Algebra >>

Exercise 9.5 : Solutions of Questions on Page Number : 406

Q1 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

A homogeneous differential equation of the form can be solved by making the substitution

A. y = vx

B. v = yx

C. x = vy

D. x = v


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

Which of the following is a homogeneous differential equation?

A.

B.

C.

D.


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 8 : Application of Integrals Next Chapter 10 : Vector Algebra >>

Exercise 9.6 : Solutions of Questions on Page Number : 413

Q1 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

The integrating factor of the differential equation is

A. e–x

B. e–y

C.

D. x


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q18 :  

The integrating factor of the differential equation.

is

A.

B.

C.

D.


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 8 : Application of Integrals Next Chapter 10 : Vector Algebra >>

Exercise Miscellaneous : Solutions of Questions on Page Number : 419

Q1 :  

For each of the differential equations given below, indicate its order and degree (if defined).

(i)

(ii)

(iii)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

(i)

(ii)

(iii)

(iv)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Form the differential equation representing the family of curves given by where a is an arbitrary constant.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Prove that is the general solution of differential equation, where c is a parameter.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Find the general solution of the differential equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Show that the general solution of the differential equation is given by (x + y + 1) = A (1 – x – y – 2xy), where A is parameter


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

Find the equation of the curve passing through the point whose differential equation is,


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Find the particular solution of the differential equation

, given that y = 1 when x = 0


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Solve the differential equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

Find a particular solution of the differential equation, given that y = – 1, when x = 0 (Hint: put x – y = t)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

Solve the differential equation


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  

Find a particular solution of the differential equation , given that y = 0 when


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  

Find a particular solution of the differential equation, given that y = 0 when x = 0


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was 20000 in 1999 and 25000 in the year 2004, what will be the population of the village in 2009?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

The general solution of the differential equation is

A. xy = C

B. x = Cy2

C. y = Cx

D. y = Cx2


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

The general solution of a differential equation of the type is

A.

B.

C.

D.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q18 :  

The general solution of the differential equation is

A. xey + x2 = C

B. xey + y2 = C

C. yex + x2 = C

D. yey+ x2 = C


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 8 : Application of Integrals Next Chapter 10 : Vector Algebra >>

Maths Part-2 - Maths : CBSE NCERT Exercise Solutions for Class 12th for Differential Equations ( Exercise 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

Popular Articles