RD SHARMA SOLUTION CHAPTER – 22 Differential Equations I CLASS 12TH MATHEMATICS-EDUGROWN

Chapter 22 Differential Equations Exercise Ex. 22.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Determine the order and degree of the following differential equations. State also whether they are linear or non-linear.

Solution 27

The order of a differential equation is the order of the highest order derivative appearing in the equation.

The degree of a differential equation is the degree of the highest order derivative.

Consider the given differential equation

In the above equation, the order of the highest order derivative is 1.

So the differential equation is of order 1.

In the above differential equation, the power of the highest order derivative is 3.

Hence, it is a differential equation of degree 3.

Since the degree of the above differential equation is 3, more than one, it is a non-linear differential equation.

Chapter 22 – Differential Equations Exercise Ex. 22.2

Question 1

Solution 1

Question 2

Solution 2

Question 3(i)

Solution 3(i)

Question 3(ii)

Solution 3(ii)

Question 3(iii)

Solution 3(iii)

Question 3(iv)

Solution 3(iv)

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Form the differential equation having y = (sin^-1x)² + A cos ^-1 x + B, where A and B are arbitrary constants, as its general solution.Solution 14

Question 15(i)

Solution 15(i)

Question 15(ii)

Solution 15(ii)

Question 15(iii)

Solution 15(iii)

Question 16(i)

Solution 16(i)

Question 16(ii)

Solution 16(ii)

Question 16(iii)

Solution 16(iii)

Question 16(iv)

Represent the following family of curves by forming the corresponding differential equation (a,b being parameters):

x² + (y – b)² = 1Solution 16(iv)

Question 16(v)

Solution 16(v)

Question 16(vi)

Solution 16(vi)

Question 16(vii)

Solution 16(vii)

Question 16(viii)

Solution 16(viii)

Question 16(ix)

Solution 16(ix)

Question 16(x)

Solution 16(x)

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Chapter 22 – Differential Equations Exercise Ex. 22.3

Question 1

Solution 1

Question 2

Solution 2

Question 3

show that y = ae²x + be^-x is a solution of the differential equation Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Verify that y =  + b is a solution of the differential equation Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Show that y = e^x(A cos x + B sin x) is the solution of the differential equation

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Show that y = e^-x + ax + b is solution of the differential equation Solution 20

Question 21(i)

For the following differential equation verify that the accompanying function is a solution in the mentioned domain (a, b are parameters) Solution 21(i)

Question 21(ii)

Solution 21(ii)

Question 21(iii)

Solution 21(iii)

Question 21(iv)

Solution 21(iv)

Question 21(v)

Solution 21(v)

Chapter 22 – Differential Equations Exercise Ex. 22.4

Question 1

Solution 1

Question 2

Solution 2

Question 3

For the following initial value problem verify that the accompanying function is a solution:

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Chapter 22 – Differential Equations Exercise Ex. 22.5

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solve the following differential equation:

(sin x + cos x)dy + (cos x – sin x) dx = 0Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solve the following differential equation:

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solve the following differential equation

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

solve the following differential equation

Solution 26

Chapter 22 – Differential Equations Exercise Ex. 22.6

Question 1

Solve the following differential equation:

Solution 1

Question 2

Solve the following differential equation:

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Chapter 22 – Differential Equations Exercise Ex. 22.7

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solve the following differential equation:

Solution 35

Question 36

Solve the following differential equation:

Solution 36

Question 37(i)

Solution 37(i)

Question 37(ii)

Solve the following differential equation:

Solution 37(ii)

Question 38(i)

Solution 38(i)

Question 38(ii)

Solution 38(ii)

Question 38(iii)

ye^x/y dx = (xe^x/y + y²) dy, y ¹ 0Solution 38(iii)

Question 38(iv)

(1 + y²) tan^-1 x dx + 2y (1 + x²)dy = 0Solution 38(iv)

Question 39

Solution 39

Question 40

Solution 40

Question 41

Solution 41

Question 42

Solution 42

Question 43

Solution 43

Question 44

Solution 44

Question 45(i)

Solution 45(i)

Question 45(ii)

Solution 45(ii)

Question 45(iii)

Solution 45(iii)

Question 45(iv)

Solution 45(iv)

Question 45(v)

Solution 45(v)

Question 45(vi)

Solve the following initial value problem

=1 + x² + y² + x²y², y(0) = 1Solution 45(vi)

Question 45(vii)

Solve the following initial value problem

Solution 45(vii)

Question 45(viii)

Solution 45(viii)

Question 45(ix)

Solution 45(ix)

Question 46

Solution 46

Question 47

Solution 47

Question 48

Solution 48

Question 49

Find the particular solution of e= x + 1, given that y = 3 when x = 0.Solution 49

Question 50

Solution 50

Question 51

Solution 51

Question 52

Find the equation of a curve passing through the point (0,0) and whose differential equation is Solution 52

Question 53

Solution 53

Question 54

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 after t seconds.Solution 54

Question 55

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 (log_e 2 = 0.6931).Solution 55

Let p, t and represent the principal, time, and rate of interest respectively.

It is given that the principal increases continuously at the rate of r% per year.

Integrating both side, we get:

Question 56

Solution 56

Question 57

Solution 57

..Question 58

Solution 58

Chapter 22 – Differential Equations Exercise Ex. 22.8

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solve the following differential equation.

Solution 11

Chapter 22 – Differential Equations Exercise Ex. 22.9

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solve the following differential equation:

Solution 4

Question 5

Solve the following differential equation:

Solution 5

Question 6

Solve the following initial value problem

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solve the following initial value problem

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solve the following initial value poblem

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solve the following differential equation:

Solution 35

Question 36(i)

Solution 36(i)

Question 36(ii)

Solution 36(ii)

Question 36(iii)

Solve the following initial value problem

Solution 36(iii)

Question 36(iv)

Solution 36(iv)

Question 36(v)

Solution 36(v)

Question 36(vi)

Solution 36(vi)

Question 36(vii)

Solution 36(vii)

Question 36(viii)

Solution 36(viii)

Question 36(ix)

Solve the following initial value problem

Solution 36(ix)

Question 37

Solution 37

Question 38

Solution 38

Question 39

Solution 39

Chapter 22 – Differential Equations Exercise Ex. 22.10

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solve the following differential equation:

Solution 30

Question 31

Solve the following differential equation:

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solution 35

Question 36(i)

Solution 36(i)

Question 36(ii)

Solution 36(ii)

Question 36(iii)

Solution 36(iii)

Question 36(iv)

Solution 36(iv)

Question 36(v)

Solution 36(v)

Question 36(vi)

Solution 36(vi)

Question 36(vii)

Solution 36(vii)

Question 36(viii)

Solution 36(viii)

Question 36(ix)

Solution 36(ix)

Question 36(x)

Solution 36(x)

Question 36(xi)

Solution 36(xi)

Question 36(xii)

Solution 36(xii)

Question 37(i)

Solution 37(i)

Question 37(ii)

Solution 37(ii)

Question 37(iii)

Solution 37(iii)

Question 37(iv)

Solution 37(iv)

Question 37(v)

Solve the following initial value problem:

Solution 37(v)

Question 37(vi)

Solution 37(vi)

Question 37(vii)

Solution 37(vii)

Question 37(viii)

Solve the following initial value problem

Solution 37(viii)

Question 37(ix)

Solution 37(ix)

Question 37(x)

Solution 37(x)

Question 37(xi)

Solution 37(xi)

Question 37(xii)

dy = cos x (2 – y cosec x) dxSolution 37(xii)

Question 38

Solution 38

Question 39

Solution 39

Question 40

Solve the differential equation

Solution 40

Question 41

Solution 41

Chapter 22 – Differential Equations Exercise Ex. 22.11

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Chapter 22 – Differential Equations Exercise Ex. 22RE

Question 1(i)

Solution 1(i)

Question 1(ii)

Solution 1(ii)

Question 1(iii)

Solution 1(iii)

Question 1(iv)

Solution 1(iv)

Question 1(v)

Solution 1(v)

Question 1(vi)

Solution 1(vi)

Question 1(vii)

Solution 1(vii)

Question 2

Solution 2

Question 3(i)

Solution 3(i)

Question 3(ii)

Solution 3(ii)

Question 3(iii)

Solution 3(iii)

Question 3(iv)

Solution 3(iv)

Question 3(v)

Solution 3(v)

Question 3(vi)

Solution 3(vi)

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solution 35

Question 36

Solution 36

Question 37

Solution 37

Question 38

Solution 38

Question 39

Solution 39

Question 40

Solution 40

Question 41

Solution 41

Question 42

Solution 42

Question 43

Solution 43

Question 44

Solution 44

Question 45

Solution 45

Question 46

Solve the following differential equation:

Solution 46

Question 47

Solution 47

Question 49

Solution 49

Question 50

Solution 50

Question 51

Solution 51

Question 52

Solution 52

Question 53

Solution 53

Question 54

Solution 54

Question 55

Solution 55

Question 56

Solution 56

Question 57

Solution 57

Question 58

Solution 58

Question 59

Solution 59

Question 60

Solution 60

Question 61

Solution 61

Question 62

Solution 62

Question 63

Solution 63

Question 64(i)

Solution 64(i)

Question 64(ii)

Solution 64(ii)

Question 64(iii)

Solution 64(iii)

Question 64(iv)

Solution 64(iv)

Question 64(v)

Solution 64(v)

Question 64(vi)

Solution 64(vi)

Question 65(i)

Solution 65(i)

Question 65(ii)

Solution 65(ii)

Question 65(iii)

Solution 65(iii)

Question 66(i)

Solution 66(i)

Question 66(ii)

Solution 66(ii)

Question 66(iii)

Solution 66(iii)

Question 66(iv)

Solution 66(iv)

Question 66(v)

Solution 66(v)

Question 66(vi)

Solution 66(vi)

Question 66(vii)

Solution 66(vii)

Question 66(viii)

Solution 66(viii)

Question 66(ix)

Solution 66(ix)

Question 66(x)

Solution 66(x)

Question 66(xi)

Solution 66(xi)

Question 66(xii)

Solution 66(xii)

Question 66(xiii)

Solution 66(xiii)

Question 66(xiv)

Solution 66(xiv)

Question 66(xv)

Solution 66(xv)

Question 67(i)

Solution 67(i)

Question 67(ii)

Solution 67(ii)

Question 67(iii)

Solution 67(iii)

Question 68

Solution 68

Question 69

Solution 69

Question 70

Solution 70

Question 71

Solution 71

Question 72

Solution 72

Question 73

Solution 73

Question 74

Solution 74

Question 75

Solution 75

Question 76

Solution 76

Question 77

Solution 77

Question 78

Solution 78

Question 79

Solution 79