Differential Equations NCERT Solutions Math Class 12 CBSE

Question 1

Determine order and degree(if defined) of differential equation

Question 2

Determine order and degree(if defined) of differential equation

NCERT Question Solutions

Question 3

Determine order and degree(if defined) of differential equation

Question 4

Determine order and degree(if defined) of differential equation

Question 5

Determine order and degree(if defined) of differential equation

Question 6

Determine order and degree(if defined) of differential equation

Question 7

Determine order and degree(if defined) of differential equation

Question 8

Determine order and degree(if defined) of differential equation

Question 9

The degree of the differential equation

is

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

Question 10

The order of the differential equation

is

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

Question 11

Determine order and degree(if defined) of differential equation

Question 12

Determine order and degree(if defined) of differential equation

Question 13

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

(i)

(ii)

(iii)

Question 14

Question 15

Question 16

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

Question 17

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

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

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

A.

B.

C.

D.

Question 27

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)

Question 28

Question 29

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

Question 30

Which of the following differential equations hasas the general solution?

A.

B.

C.

D.

Question 31

Question 32

Question 33

Question 34

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

Question 35

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

Question 36

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

Question 37

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

Question 38

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

Question 39

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

Question 40

Question 41

Question 42

Question 43

Question 44

Question 45

Question 46

Question 47

Question 48

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

Question 49

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

Question 50

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.

Question 51

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).

Question 52

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.

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60

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).

Question 61

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.

Question 62

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?

Question 63

The general solution of the differential equation

A.

B.

C.

D.

Question 64

Solve the differential equation

Question 65

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

Question 66

Find the general solution of the differential equation

Question 67

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

Question 68

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

Question 69

Find the particular solution of the differential equation

, given that y = 1 when x = 0

Question 70

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?

Question 71

The general solution of the differential equation is

A. xy = C

B. x = Cy2

C. y = Cx

D. y = Cx2

Question 72

Question 73

Question 74

Question 75

Question 76

Question 77

Question 78

Question 79

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

Question 80

Question 81

Question 82

Question 83

Question 84

Question 85

Question 86

Question 87

Question 88

Which of the following is a homogeneous differential equation?

A.

B.

C.

D.

Question 89

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

Question 90

Question 91

Question 92

Question 93

Question 94

Question 95

Question 96

Question 97

Question 98

Question 99

Question 100

Question 101

Question 102

Question 103

Question 104

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.

Question 105

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.

Question 106

The integrating factor of the differential equation is

A. ex

B. ey

C.

D. x

Question 107

The integrating factor of the differential equation.

is

A.

B.

C.

D.

Question 108

Question 109

Solve the differential equation

Question 110

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

Question 111

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

Question 112

The general solution of a differential equation of the type is

A.

B.

C.

D.

Question 113

The general solution of the differential equation is

A. xey + x2 = C

B. xey + y2 = C

C. yex + x2 = C

D. yey + x2 = C

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