Class 12-commerce RD SHARMA Solutions Maths Chapter 22 - Differential Equations
Differential Equations Exercise Ex. 22.1
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Solution 20
Solution 22
Solution 23
Solution 24
Solution 25
Solution 26
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.
Differential Equations Exercise Ex. 22.2
Solution 1
Solution 2
Solution 3(i)
Solution 3(ii)
Solution 3(iii)
Solution 3(iv)
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15(i)
Solution 15(ii)
Solution 15(iii)
Solution 16(i)
Solution 16(ii)
Solution 16(iii)
Solution 16(iv)
Solution 16(v)
Solution 16(vi)
Solution 16(vii)
Solution 16(viii)
Solution 16(ix)
Solution 16(x)
Solution 17
Solution 18
Solution 19
Differential Equations Exercise Ex. 22.3
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Solution 20
Solution 21(i)
Solution 21(ii)
Solution 21(iii)
Solution 21(iv)
Solution 21(v)
Differential Equations Exercise Ex. 22.4
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Differential Equations Exercise Ex. 22.5
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Solution 20
Solution 21
Solution 22
Solution 23
Solution 24
Solution 25
Solution 26
Differential Equations Exercise Ex. 22.6
Solution 1
Solution 2
Solution 3
Solution 4
Differential Equations Exercise Ex. 22.7
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Solution 20
Solution 21
Solution 22
Solution 23
Solution 24
Solution 25
Solution 26
Solution 27
Solution 28
Solution 29
Solution 30
Solution 31
Solution 32
Solution 33
Solution 34
Solution 35
Solution 36
Solution 37(i)
Solution 37(ii)
Solution 38(i)
Solution 38(ii)
Solution 38(iii)
Solution 38(iv)
Solution 39
Solution 40
Solution 41
Solution 42
Solution 43
Solution 44
Solution 45(i)
Solution 45(ii)
Solution 45(iii)
Solution 45(iv)
Solution 45(v)
Solution 45(vi)
Solution 45(vii)
Solution 45(viii)
Solution 45(ix)
Solution 46
Solution 47
Solution 48
Solution 49
Solution 50
Solution 51
Solution 52
Solution 53
Solution 54
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:
Solution 56
Solution 57
.
Solution 58
Differential Equations Exercise Ex. 22.8
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Differential Equations Exercise Ex. 22.9
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Solution 20
Solution 21
Solution 22
Solution 23
Solution 24
Solution 25
Solution 26
Solution 27
Solution 28
Solution 29
Solution 30
Solution 31
Solution 32
Solution 33
Solution 34
Solution 35
Solution 36(i)
Solution 36(ii)
Solution 36(iii)
Solution 36(iv)
Solution 36(v)
Solution 36(vi)
Solution 36(vii)
Solution 36(viii)
Solution 36(ix)
Solution 37
Solution 38
Solution 39
Differential Equations Exercise Ex. 22.10
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Solution 20
Solution 21
Solution 22
Solution 23
Solution 24
Solution 25
Solution 26
Solution 27
Solution 28
Solution 29
Solution 30
Solution 31
Solution 32
Solution 33
Solution 34
Solution 35
Solution 36(i)
Solution 36(ii)
Solution 36(iii)
Solution 36(iv)
Solution 36(v)
Solution 36(vi)
Solution 36(vii)
Solution 36(viii)
Solution 36(ix)
Solution 36(x)
Solution 36(xi)
Solution 36(xii)
Solution 37(i)
Solution 37(ii)
Solution 37(iii)
Solution 37(iv)
Solution 37(v)
Solution 37(vi)
Solution 37(vii)
Solution 37(viii)
Solution 37(ix)
Solution 37(x)
Solution 37(xi)
Solution 37(xii)
Solution 38
Solution 39
Solution 40
Solution 41
Differential Equations Exercise Ex. 22.11
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Solution 20
Solution 21
Solution 22
Solution 23
Solution 24
Solution 25
Solution 26
Solution 27
Solution 28
Solution 29
Solution 30
Solution 31
Solution 32
Solution 33
Solution 34
Differential Equations Exercise Ex. 22RE
Solution 1(i)
Solution 1(ii)
Solution 1(iii)
Solution 1(iv)
Solution 1(v)
Solution 1(vi)
Solution 1(vii)
Solution 2
Solution 3(i)
Solution 3(ii)
Solution 3(iii)
Solution 3(iv)
Solution 3(v)
Solution 3(vi)
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Solution 20
Solution 21
Solution 22
Solution 23
Solution 24
Solution 25
Solution 26
Solution 27
Solution 28
Solution 29
Solution 30
Solution 31
Solution 32
Solution 33
Solution 34
Solution 35
Solution 36
Solution 37
Solution 38
Solution 39
Solution 40
Solution 41
Solution 42
Solution 43
Solution 44
Solution 45
Solution 46
Solution 47
Solution 49
Solution 50
Solution 51
Solution 52
Solution 53
Solution 54
Solution 55
Solution 56
Solution 57
Solution 58
Solution 59
Solution 60
Solution 61
Solution 62
Solution 63
Solution 64(i)
Solution 64(ii)
Solution 64(iii)
Solution 64(iv)
Solution 64(v)
Solution 64(vi)
Solution 65(i)
Solution 65(ii)
Solution 65(iii)
Solution 66(i)
Solution 66(ii)
Solution 66(iii)
Solution 66(iv)
Solution 66(v)
Solution 66(vi)
Solution 66(vii)
Solution 66(viii)
Solution 66(ix)
Solution 66(x)
Solution 66(xi)
Solution 66(xii)
Solution 66(xiii)
Solution 66(xiv)
Solution 66(xv)
Solution 67(i)
Solution 67(ii)
Solution 67(iii)
Solution 68
Solution 69
Solution 70
Solution 71
Solution 72
Solution 73
Solution 74
Solution 75
Solution 76
Solution 77
Solution 78
Solution 79
Differential Equations Exercise MCQ
Solution 1
Correct option: (c)
Solution 2
Correct option: (b)
Solution 3
Correct option: (b)
Solution 4
Correct option:(b)
Degree is the power of highest order derivative.
Highest order is 2 and its power is 2.
Hence, degree of differential equation is 2.
Solution 5
NOTE: Answer not matching with back answer.
Solution 6
Correct option:(d)
Solution 7
Correct option: (c)
Solution 8
Correct option: (a)
Solution 9
Correct option: (c)
Here, constants are c1, c2, c3, c4, c5, c6.
But c3+c4 is also constant. Hence, total 5 constants.
Solution 10
Correct option: (b)
Solution 11
Correct option: (a)
Solution 12
Correct option: (a)
Solution 13
Correct option: (a)
Differential equation contains only one constant hence,
Order of differential equation is 1.
Solution 14
Correct option: (b)
Solution 15
Correct option: (b)
Solution 16
Correct option: (d)
Solution 17
Correct option: (a)
Solution 18
Correct option: (a)
Solution 19
Correct option: (c)
Solution 20
Correct option: (d)
Solution 21
Correct option: (b)
Solution 22
Correct option: (b)
Solution 23
Correct option: (d)
Note: log is considered same as ln.
Solution 24
Correct option: (c)
Solution 25
Correct option:(a)
Solution 26
Correct option: (b)
Solution 27
Correct option: (d)
Solution 28
Correct option: (d)
Solution 29
Correct option: (a)
Solution 30
Correct option:(a)
Solution 31
Correct option:
Solution 32
Correct option: (b)
Solution 33
Correct option:(c)
Solution 34
Correct option: (d)
Solution 35
Correct option: (b)
Solution 36
Correct option:(d)
Solution 37
Correct option: (c)
Note: Answer not matching with back answer.
Solution 38
Correct option: (c)
Solution 39
Correct option: (a)
Solution 40
Correct option: (c)
Solution 41
Correct option: (d)
Highest order derivative is 2 but equation cannot be expressed as a polynomial in differential equation.
Hence, it is not defined.
Solution 42
Correct option:(a)
Highest order of the derivative is 2.
Solution 43
Correct option: (d)
In the general solution of differential equation of order n has n number of arbitrary constants.
Solution 44
Correct option: (d)
The number of arbitrary constants in the particular solution of a differential equation of third order is always zer0.
Solution 45
Correct option: (b)
Solution 46
Correct option: (c)
Solution 47
Correct option: (a)
Solution 48
Correct option: (c)
Solution 49
Correct option: (d)
Solution 50
Correct option: (c)
Solution 51
Correct option:(d)
Solution 52
Correct option:(c)
Solution 53
Correct option: (c)
Solution 54
Correct option: (c)
Differential Equations Exercise Ex. 22VSAQ
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Solution 20
Solution 21
