Polytechnic Mathematics
452 videos • 242 views • by Doctor of Mathematics
1
Find the Laplace Transform of the following function t. cosat.
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2
H-54:L{sin5t+cos3t}
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3
Solve d^2y/dx^2+y=x.cos2x by using Laplace transform
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4
Solve: xy(1+xy^2)dy/dx =1
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5
L{t^2.cosat}
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6
Solve: dy/dx=x+y+1/x-y (watch this video carefully because I have committed a mistake at time 7:18)
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7
Solve: dy/dx=(x+y+1) /(3x+2y+3)
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8
(x-y-2)dx =(2x-2y-3) dy
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9
(7x-3y+3) dy+(3y-7x+7) dx=0
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10
Solve: sinydy/dx+cosy=x
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11
Solve :(x^2+y^2+2xy+1)dy/dx=x+y
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12
Solve: (D^2-2D+5) ^2=0 Linear Differential equation of higher order but constant coefficients
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13
If u=sin-1(√x-√y/√x+√y) , prove that ∂u/∂x=-y/x.u∂/∂y
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14
If u=cos-1(x+y/√x+√y) , prove that xdelu/delx+ydelu/dely+1/2.cotu=0
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15
If u=tan-1(x²+y²/x+y), prove that x∂u/∂x+y∂u/∂y=1/2.sin2u
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16
Verify Euler's theorem for the homogenous function:u=x^n.log(y/x)
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17
If u=ax²+2hxy+by², prove that x∂u/∂x+y∂u/∂y=2u
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18
If u=sin-1(x+y/√x+√y) , prove that xdelu/delx+ydelu/dely=1/2.tanu
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19
Verify Euler's theorem for the function u=1/√(x^2+y^2)
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20
L{t.sinat}=?
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21
If u=log[(x^3+y^3) /(x+y)] , prove that x.delu/x+y.delu/dely=2.
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22
If u=x^2y^2/(x^2+y^2), prove that
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23
u=x²y²/(x²+y²), prove that x²∂²u/∂x²+2xy∂²u/∂x∂y+y²∂²u/∂y²=2u.
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24
If u=tan-1y/x, prove that x∂u/∂x+y∂u/∂y=0
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25
Solve: xdy-ydx+a(x^2+y^2) =0
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26
Solve: (3x+y-5)dy=2 (x+y-1)dx
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27
Find the particular Integral of (D^2+a^2) y=sinax; a=/0
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28
Solve: z(y^2.p-x^2.q)= x^2y
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29
Find the unit vector normal to the surface x2.y+2xz=4 at the point (2,-2,3).
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30
Select any two distinct matrices A and B of order 2 x2 with real entries of your choice. verify rank
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31
Find: L-1{p/(p^4+p^2+1)}
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32
Evaluate:B(1,2)+B(2,1) (Beta function)
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33
B(m+1,n) /B(m, n)
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34
J-10:Integrate from θ=0 to θ=π/2 sin^7θ.√cosθ in term of beta function.
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35
Evaluate:B(1/2,1/2) where B is beta function
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36
Show that arc of the upper half of the curve r=a(1-cosθ) is bisected by θ=2π/3.
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37
Find the area included between the parabolae y^2=4ax and x^2=4by||Top mathematics channel on YouTube
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38
Solve: d^2y/dx^2-3dy/dx=2sin3x
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39
Solve: sin2x.dy/dx=y+tanx
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40
Prove that integration from 0 to 2a f(x)=2 x integration from 0 to a of f(x) w. r. t. x P6(Prop.)
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41
Solve:(x+y-a/x+y-b)dy/dx=(x+y+a/x+y+b)
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42
Solve: dy/dx+1=e^x-y
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43
Solve: d^2y/dx^2-3dy/dx+2y=e^5x or (D^2-3D+2)y=e^5x
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44
d^3y/dx^3-d^2y/dx^2-6dy/dx=1+x^2 or (D^3-D^2-6D)y=1+x^2
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45
Solve: (D^2-2D+5)y=e^2xsinx
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46
Find a complete integral of p^3+q^3-3pqz=0.(Partial Differential equation of first order)
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47
Find the complete integral of x^2p^2+y^2q^2=z^2
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48
Solve: d^2y/dx^2+a^2y=cosax or (D^2+a^2)y=cosax.
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49
Solve: (D^3+3D-4)y=xe^-2x
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50
Solve: dy/dx=(4x+y+1)^2
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51
Solve: d^2y/dx^2-y=4xe^x
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52
Find P. I. of (D^2-4DD'+4D'^2+D-2D')z=e^x+y
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53
Solve: d^3y/dx^3+d^2y/dx^2-dy/dx-y=cos2x.
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54
If aij=aji, show that A=[aij] is symmetric matrix.
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55
Check the following function for x=05, f(x)=e^1/x-1/e^1/x+1
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56
Solve D. E. : d^2y/dx^2+y=x^3+e^x+sinx
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57
Test the continuity and differentiabelity of the function f(x) at x=2 where f(x)=1+x for x less than
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58
Solve D. E. :(D^2+2D+1)y=xcosx
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59
Solve D. E. :(D^2+1)y=xe^2x. L-2
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60
Evaluate limit (3x+|x|)/(7x-5|x|)
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61
Show that limit sinax/sinbx=a/b
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62
Solve: d^2y/dx^2+a^2y=cosax
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63
Solve:d^3y/dx^3+a^2dy/dx=sinax
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64
Solve: (D^-3D+2)y=e^x
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65
Solve:d^3y/dx^3+3d^2y/dx^2+3dy/dx+y=e^-x. (Please see description)
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66
Solve: (D+2)(D-1)^3y=e^x
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67
Solve: (xtany/x-ysec^2y/x)dx+xsec^2y/x=0
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68
Solve: d^3y/dx^3+3d^2y/dx^2+2dy/dx=x^2 or D^3y+3D^2y+2Dy=x^2
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69
Find first order partial derivative of u w. r. t. x if u=y^x.
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70
Apply the method of Laplace transform to solve differential equation: d^2x/dt^2-2dx/dt+x=e^t with x=
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71
Solve: d^2y/dx^2+y=cos2x
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72
Solve: (D^2+D-6)y=x
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73
x(x-1)dy/dx-(x-2)y=x^3(2x-1)
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74
Solve: d^2y/dx^2+dy/dx+y=e-x
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75
Solve: y=apx+bp^3
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76
Solve:d^2/dx^2-5dy/dx+6y=e^4x or (D^2-5D+6)y=e^4x
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77
Solve: d^4y/dx^4-a^4y=0 or (D^4-a^4)y=0
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78
Solve: (D^4+8D^2+16)y=0
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79
Solve: d^3y/dx^3-3d^2y/dx^2+4y=0
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80
Solve: d^2y/dx^2-4dy/dx+4y=xe^2x or (D^2-4D+4)y=xe^2x
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81
Solve:(D^4-4D+4)y=0
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82
Solve: d^2y/dx^2-7dy/dx+12=0 or (D^2-7D+12)y=0
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83
Second derivative of {3/(s^2+9)} w. r. t. s
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84
Using Laplace transform to solve D. E. d^2y/dt^2-3dy/dt+2y=4t+e^3t
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85
Evaluate: ∫1/(1+x^2) √(1-x^2) dx
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86
Evaluate: ∫1/(1+x^3)dx
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87
Solve:d^2y/dx^2-4y=x^2
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88
(2x+3y+4)dy=(x+2y-3)dx
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89
Solve: (x+2)^2d^2y/dx^2-(x+2)dy/dx +y=3x+4
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90
Solve: d^2y/dx^2+4y=xsinx
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91
Solve : d^2y/dx^2+4y=xsinx
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92
The area bounded by the curves x^2+y^2=2x and x^2+y^2=4x,and the straight lines y=x and y=0 is:(A)3(
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93
Solve : xe^(x^2+y^2) +y(^(x^2+y^2)+1)dy=0
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94
limit (a^xsinbx-b^xsinax) /(tannx-tanax)
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95
limit a tends to b (a^xsinbx-b^xsinax) /(tannx-tanax)
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96
Find the shortest distance between the lines (x-3)/3=(y-8)/-1=(z-3)/1and (x+3)/-3=(y+7)/2=(z-6)/4
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97
√(a^2+x^2)dy/dx+y=√(a^2+x^2)-x
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98
Solve:dy/dx=(x-y+1)/(x+y-3)
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99
If y=sin-1x/√1-x^2 , show that (1-x^2)yn+2-(2n+3)xyn+1-(n+1)^2yn=0
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100
If y=e^tan-1x , prove that (1+x^2) yn+2+{2(n+1)x-1}yn+1+n(n+1)yn=0
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101
If y=cos(logx) prove that x^2yn+2+(2n+1)xyn+1+(n^2+1)yn=0
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102
∫x^7/√(a^2-x^2) =16/35a^7 limit x=0 to x=a
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103
Prove that: (axb)x(cxd)+(axc)x(dxb)+(axd)x(bxc) =2[b d c]a ||Top B Sc.Mathematics on YouTube free
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104
If u=f(z), z being a homogenous function of degree n in x, y, prove that
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105
If u=log(x^3+y^3+z^3-3xyz ), show that del^2u/del2+del^2u/dely^2+del^2u/delz^2=-3/(x+y+z)^2
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106
Obtain differential equation whose solution is given by Ax^2+By^2=1
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107
Solve: ty"+(t-1)y'-y=0 given that y(0)=5, y(infinity)=0
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108
Find the volume of a sphere of radius 'a' by the method of integration.
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109
Prove that the surface area of a sphere of radius 'a' is 4πa^2 by method of integration.
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110
Find the eigen values and corresponding eigen vectors of the matrix [1 1 1,1 2 3,-1 1 0]
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111
Separate real and imagine parts exp(siniθ)
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112
For Iradication of confusion in (A+B)X(A-B)=2BXA
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113
Solve : (2x-4y+5)dy+(x-2y+3)dx=0
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114
If y=A/x+Bx, where A and B are constant, show that x^2d^2y/dx^2+xdy/dx=y
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115
Solve:(D^2+m^2)x=acosnt, if x=x°, Dx=x1 when t=0, n≠m
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116
If u=sin-1x/y+tan-1y/x, show that xdel u/del x+ydel u/del y=0
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117
as If u=(1-2xy+y^2)^-1/2, prove that xdelu/d elx-y delu/dely=y^2u^3
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118
Solve the initial value problem dy/dx=2-e^x/3+2y and determine where the solution attains it's maxim
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119
If u=(1-2xy+y^2)^-1/2 , prove that del/delx[(1-x^2)delu/delx]+del/dely[y^2delu/dely]=0
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120
(x^2-y^2)dy/dx=2xy
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121
Evaluate: ∇^2(1/r) del^2(1/r) or div.(grad1/r)
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122
Solve:dy/dx=3y-x+7/x-7y-3
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123
Prove that if f(x, y)=1/√y.e^-(x-a)^2/4y, fxy(x, y)=fyx(x,y)
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124
To prove: Gamma(1/2)=√π or Γ1/2
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125
Find the whole area of the curve a^2y^2=x^3(2a-x)
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126
Ifz=(x+y)+(x+y)Φ(y/x), then prove that x(d^2z/dx^2-d^2z/dxdy)=y(d^2y/dy^2-d^2z/dxdy) all partial
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127
Relation between polar and Cartesian coordinates
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128
If z(z^2+3x)+3y=0, prove that d^2z/dx^2+d^2z/dy^2=2z(x-1)/(z^2+x)^3 all partial doffferentiation
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129
Evaluate ∫dθ/(1-sin^4θ)
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130
Form the differential equation of the system of circles touching the y-axis at the origin.
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131
Solve: dy/dx=sinx.siny
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132
Solve: dy/dx=ye^x
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133
Solve: dy/dx=e^ax.cosby
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134
Solve: (1+y^2)dx-(1+x^2)dy=0
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135
Solve: (x^2-yx^2)dy/dx+y^2+xy2=0
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136
If z^3-3yz-3x=0,. show that zdz/dx=dx/dy,z[d^2z/dxdy+(dx/dx)^2]=d^2z/dy^2 all partial differentiatio
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137
If u(x,y,z)=1/(x^2+y^2+z^2), find the value of d^2u/dx^2+d^2u/dy^2+d^2u/dz^2 all partial differentia
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138
Find curl V,where V=e^xyz(i+j+k)
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139
∫x^4e-xdx from 0 to infinity
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140
Evaluate ∫e-4x.x^3/2dx from 0 to infinity
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141
Evaluate ∫ tan^nxdr,from x=0 to π/2
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142
Prove that in triangle ABC,. Area(ABC)=abc/4R
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143
Find the area of the surface of revolution formed by revolving the curve r=a(1+cosθ) about the init
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144
Prove: div.r=3. or ∇.r=3
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145
Expand log(1+x) by Maclaurin's theorem.
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146
Find the sum up to n terms of the series 5+55+555+........
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147
Sanam Bewafa - Part 16 Of 16 - Salman Khan - Chandni - Superhit Bollywood Film
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148
Solve:(1+e^x/y)dx+e^x/y(1-x/y)=0 in Hindi Urdu
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149
Solve: dy/dx+x-2y/2x-y=0
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150
verify stokes'theorem for A=(y-z+2)I+(y-z+4)j -xzk,S is surface of cube x=0,y =0,z=0,x =2,y=2,z=2
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151
Lo Chali Main - Hum Aapke Hain Koun - Salman Khan, Madhuri Dixit & Renuka Shahane
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152
A particle of mass m moves in the xy-plan , r=acos(wt)i+bsin(wt)j.(a)The particle moves in ellipse
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153
Solve:x^2d^2y/dx^2-3vxdy/dx+4y=2x^2 Homogeneous linear diffential equation
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154
Find Laplace transform of the 3e^2t+4e^-3t
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155
Find :L[3sin2t-5cos2t]
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156
Determine Laplace of sint.cost
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157
Determine L[cosh^2(2t)]
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158
Find the Laplace transform of cosat/t
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159
Find the Laplace transform of sinat/t
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160
Solve:(x^2D^2+xD-1)y=x^2e^x
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161
For the Heaviside's unit step function f(t-a)={1,t greater than a;0,t less than a,prove that L[F(t
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162
Find L{sinht/t} Laplace transform
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163
Prove that ∫t^3.e^-t.sintdt from t=0 to t=♾️ infinity
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164
If L{2√(t/π)}=1/p^3/2,then prove that L{1/√(πt)}=1/p^1/2
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165
If F(t) is a periodic function with period w,then L{F(t)}=1/(1-e^-pw)∫e^-pt.F(t)dt, from t=0 to t=w.
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166
Find Laplace transform of ∫(1-e-2x/x)dx from x=0 to x=t.
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167
Find L-1{1/(s-2)+1/(s+5)+6/s^4}
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168
Evaluate:L-1{1/s^2(s^2+1)}
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169
Evaluate:L-1{(3p+1)/(p+1)(p^2+1)}.
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170
Prove that ∫e^-x^2dx=√π/2
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171
Find:L-1{1/(p^2+8p+16)}
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172
First Shifting Property:If L-1{f(x)}=F(t),then L-1{f(p-a)}=e^at.F(t).
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173
Find L-1{1/(p+3)^7/2}
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174
second shifting property: If L-1{f(p)}=F(t),then L-1{e^-ap.f(p)}=G(t),where G(t)={F(t-a), greater th
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175
यदि u=f(r)तथा x=cos,y=rsin तो सिद्ध करें del^2/delx^2+del^2u/dely^2=f(r)+1/rf'(r)
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176
यदि r=ae^nt+be^nt जहां a तथा b सदिश स्थिरांक हैं तब सिद्ध करो कि d^2r/dt^2-n^2r=0.
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177
If da/dt=rxa,db/dt=rxb,then prove that d(axb)/dt=rx(axb)
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178
If u=sinθi+cosθj+θk,v=cosθ i-sinθj-3,w=2i+3j-k,find d/dθ[ux(vxw) at θ=0
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179
वक्र r=4ti+t^2j+2t^3k के बिंदुओं t=1तथा t=2 पर स्पर्श रेखाओं के बीच का कोण ज्ञात करो.
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180
Show that :∫x^c/c^xdx=c+1/l(ogc)^c+1
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181
Prove that gamma n/c^n=∫e^-cy.y^n-1dy
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182
If m and n are positive real numbers,prove that ∫x^m-1(log1/x)^n-1dx.
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183
Transformation of Gamma functions:Prove that gamma n =∫(log1/y)^n-1dy.
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184
Legendre's Duplication Formula:Γn Γ(n+1/2)=√π/2^2n-1Γ2n
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185
आव्यूह परिवर्तत ज्ञात कीजिए Find the transpose of a matrix
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186
यदि A=[0 1 2, 1 0 -1,2 -1 0]हो तो A^2 ज्ञात करो l
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187
Relation between beta and gamma functions
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188
Complement Formula
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189
वक्र r=t^2i+2tj-t^3 k के बिंदुओं t=1तथा t=-1 पर खींची गई स्पर्श रेखाओं के बीच का कोण ज्ञात कीजिए
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190
एक कण वक्र x=2तथा के अनुदेश गतिशील है तो सदिश केअनुदिश वेग तथा त्वरण के वियोजित भाग ज्ञात करें जबकि
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191
Integration of 1/(sin2x-sinx) w.r.t. x
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192
e^ax.sinbx.coscx का n वा्ं अवकल गुणांक ज्ञात करो।
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193
x/(1+3x+2x^2) का वां अवकल गुणांक ज्ञात करोFind n th derivative of x/(1+3x+2x^2)
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194
यदि r=।r। और r=xi+yj+zk then find del r=r/r
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195
(D^3+6D^2+11D+6)y=0 को हल करें। Linear diffential equations with constant coefficients
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196
Null matrix और उसके rank लिखो
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197
A-B ज्ञात करो ,यदि A=[4 2, 3 5],B=[3 7,2 5]
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198
L[4cos^2(2t)] का मान ज्ञात करो।
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199
Gamma Function की परिभाषा लिखो।
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200
L-1[1/√p] को हल करो।
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