Differential Equation(B.Sc notes)
476 videos • 5,102 views • by Doctor of Mathematics
1
Solve p.tanx+q.tany=tanz ||Best Mathematics Channel on YouTube||
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2
Solve: y^2.dy/dx=x+y^3
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3
Solve: tany.dx+tanx.dy=0
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4
Solve:Log(dy/dx)=ax+by
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5
x.cos^2(y).dx=y.cos^2(x).dy
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6
Solve:. xy.dy/dx=(1+y^2)(1+x+x^2)/(1+x^2)
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7
Solve:(2ax+x^2)dy/dx=(a^2- +2ax)
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8
Solve D.E. (y-2x)dx=(5y-6x)dy
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9
Solve D.E. (x.e^y/x-y.siny/x)dx+x.siny/x.dy=0
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10
Solve Differential Equation (6x-5y+4)dy+(y-2x-1)dx=0
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11
y.dx-x.dy=0(Solve Differential Equation)
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12
-x^2dy/dx+y+1=0 (Solve Differential Equation)
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13
dy/dx=2y (Solve Differential Equation)
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14
ydx+(1+x^2)tan-1(x)dy=0
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15
A solution of the differential equation 2x^2.d^2y/dx^2+3xdy/dx-y=0,x 0 that passes through the (1,1)
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16
Solve r+(a+b)s+abt=xy by using Monge's method.
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17
(D^2+DD'-6D'^2)z=x^2.sin(x+y)
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18
3dy/dx+2y/(x+1)=x^3/y^2 solve Differential Equation
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19
Find the orthogonal trajectory of r^n.sin(nθ)=a^n.
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20
Find the equation of the system of orthogonal trajectories of parabolas r=2a/(1+cosθ)
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21
Solve the following differential equation (a)(D^3-D^2-D-2)y=0 (b)(D^2-2aD+a^2+b^2)=0(c)(D^2+(a+b)+a)
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22
(D^2+a^2)y=x.cosax Solve Differential Equation
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23
(D^2-3D+2)y=e^x Solve differential equation
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24
(D^2+6D+9)y=2e^(-3x) Solve Differential Equation
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25
D^2y-a^2y=e^ax+e^nx Solve differential equation
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26
(D^2+D)y=1+coshx,D=d/dx;solved differentual Equation
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27
Find the differential equation corresponding toy=ae^2x+be^-3x+c.e^x , a,b, c are arbitraryconstants.
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28
Find the differential equation of all circle of radius a , or by the elimination of the constants.
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29
Find the differential equation corresponding to the family of curves y=c.(x-c)^2,where C is an arbi
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30
dy/dx=sin(x+y)+cos(x+y) Solve differential Equation
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31
Solve (y-xdy/dx)=a(y^2+dy/dx)
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32
Solve (2D^2-5DD'+2D'^2)z=5sin(2x+y)
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33
(y-x)dy/dx=a^2 Solve the differential equation ( y-x)dy/dx=a^2
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34
E-1:Solve : (x^3-3xy^2)dx=(y^3-3x^.2y)dy differential equation
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35
Solve D.E. (x^2-y^2)dx+2xydy=0
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36
What is the degree of the given differential equation:(d^2y/dx^2)+(dy/dx)^2=log(dy/dx)
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37
Find the differential equation of all circles passing through the origin and having their centre on
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38
Solve (2x+3y-5)dy/dx+(3x+2y-5)=0
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39
Solve d^2y/dx^2-x^2.dy/dx+xy=x. Differential equation of second degree with variable coefficients
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40
Solve: (D^2-5D+6)y=3sinx
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41
Solve (D^2+9)y=sec3x
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42
Find the orthogonal trajectory of the family of curve r=a+cosnθ.
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43
Solve: (2D^2D'-3DD'^2+D'3)z=0
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44
Find the general solution of the D.E. y''+2y'+3y=e^x ||Top Mathematics YouTube channel
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45
Find the general solution of the y''-3y'+4y=0.
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46
Solve x+p/√1+p^2=a differential equation of oder one but degree is not one.
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47
Solve initial value problem dy/dx+y.tanx=sin2x,y (0)=1
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48
Solve (D^2-3DD'+2D'^2)z=e^2x-y
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49
Solve x(1+y^2)dx-y(1+x^2)dy=0
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50
If z=f(x^2.y); where f is defferentiable ,then show that xdelz/delx=2ydelz/dely
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51
Solve the initial value problem d^2x/dt^2-3dx/dt+2x=0 ;x(0)=2;x'(0)=0
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52
Solve p-2q=3x^2sin(y-2x)
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53
Reduce the equation (px^2+y^2)(px+y)=(p+1)^2 to clairaut's form by using the substitution u=xy and v
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54
Solve : ty''+2y'+ty=0
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55
Find singular solution of the differential equation satisfied by family of curved c^2+2cy-x^2+1=0
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56
Apply the method of Laplace transforms to solve d^2y/dt^2+tdy/dt=y where y(0)=0 and dy/dt=1 at t=0.
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57
Solve dy/dx+ay=e^mx
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58
Show that the total differential equation (y^2+yz)dx+(z^2+zx)dy+(y^2-xy)dz=0
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59
Solve:(x+y)dx+(x-y)dy=0
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60
Find the radius of curvature at point (r,θ) of the curve r(1+cosθ)=a
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61
Solve: d^2y/dx^2+a^2y=secax
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62
Solve: (D^2+2D+1)y=2x+x^2 differential equation
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63
Solve:dx/dt+2x-3y=t,dy/dt-3x+2y=e^2t
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64
dx/dt+2dy/dt-2x+2y=3e^t; 3dx/dt+dy/dt+2x+y=4e^2t
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65
Solve:(D+D'-1) (D+D'-3) (D+D')z =e^x+y.sin(2x+y) non-homogeneous Partial Differential Equation.
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66
Solve: (D^3-2D^2+5D)y =0, y(0) =0, y'(0) =1, y(pi/8) =0
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67
Explanation of Shab-e-miraj and Isra on basis on special theory of relativity
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68
x(y^2+z) p-y(x^2+z)= z(x^2-y^2)
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69
Find a complete integral of (p+q) (px+qy) =1
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70
Find the complete integral of differential equation z=px+ qy+p^2+q^2
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71
(x-y)(xr-ys-sx+yt)=(x+y) (p-q)
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72
Solve: (1-x^2)dy/dx+xy=ax
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73
Find a complete integral of z. (p^2-q^2) =x-y.
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74
Solve: x(1-x^2)dy/dx+(2x^2-1)y=ax^3
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75
Solve (D^2+DD'+D'-1) z=sin(x+2y)
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76
Solve (D^3-3DD'+D+1)z=e^2x+3y
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77
Solve by power series method dy/dx-y=0.
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78
Solve (D-3D'-2) ^2z=2e^2x.tan(y+3x)
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79
Find the orthogonal trajectories of the system of curves given by r=a+sin5θ.
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80
(D^2-a^2D'^2) z=x
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81
Find Fourier Transform of F(x) =e^-|x| , |x| less than 1;0 if |x| greater than 1.
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82
Find the series solution in power of x of following differential equation d^2y/dx^2+xy=0
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83
Solve: s=2x+2y P. D. E.of second order
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84
Solve: y^2.dx+(x^2-xy+y^2) dy=0
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85
Solve:del2z/delxdrly+drlz/delx.f(x) =F(y) Patial differential equation of second order
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86
Solve: dy/dx+(1-2x) /x^2.y=1
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87
(D^2-5D+6) y=2e^3x+3e^2x (For complete solution see in description box)
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88
Solve D. E. dx/dy=x+2y^3/y; y(1) =2.
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89
Solve: (D^4-m^4) y=coshmx
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90
Solve: y"+y=x.cos2x, y=y'=0 when x=0.
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91
Solve: r-t. Cos^2x+p.tanx=0
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92
Solve:xy^2(xdy/dx+y) =a^2
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93
Solve: xy(1+xy^2)dy/dx =1
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94
dy/dx+(ycos+siny+y) /(sinx+xcosy+x) =0
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95
Solve :(ylogx-2)ydx =xdy
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96
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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97
Solve: dy/dx=(x+y+1) /(3x+2y+3)
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98
(x-y-2)dx =(2x-2y-3) dy
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99
(7x-3y+3) dy+(3y-7x+7) dx=0
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100
Solve: sinydy/dx+cosy=x
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101
Solve :(x^2+y^2+2xy+1)dy/dx=x+y
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102
Solve: (D^2-2D+5) ^2=0 Linear Differential equation of higher order but constant coefficients
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103
Solve Partial differential equation of second order del^2z) delxdely+delz/dex=cos(x+y) +y.sin(x+y)
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104
Solve the partial differential equation del^2/delydekx=4xsin(3xy)
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105
Solve: xdy-ydx+a(x^2+y^2) =0
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106
Solve: (3x+y-5)dy=2 (x+y-1)dx
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107
Find the particular Integral of (D^2+a^2) y=sinax; a=/0
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108
Solve: z(y^2.p-x^2.q)= x^2y
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109
Solve:(x+y^2)p+yq =z+x^2
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110
t+s+q=0 (Partial differential equation of second order)
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111
r-sin^2(x).t-cotx.p=0
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112
Solve: y^2.dx+(x^2-xy+y^2) dy=0 by making exact Differential equation
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113
(D^3-3D^2+4D-2) y=e^x+cosx
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114
(2x+3y-5)dy+ (2x+5y-1)dx=0
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115
Solve: 3p^2y^2-2xyp+4y^2-x^2=0
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116
Solve: p2-5p+6=0
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117
Solve: (2x+3y-5)dy= (x+2y-3) dx
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118
Solve: (D^2-1) y=x^2.cosx or d^2y/dx^2-y=x^2.cosx
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119
Solve: (D^4-4D^3-5D^2-36D-36)y=0
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120
Solve: (x^3y^2+xy)dx=dy
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121
ds/dx+x^2=x^2.e^3s
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122
Solve:(D^2-4D+4)y=8x^2e^2x.sin2x
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123
Prove that: integrate -1 to+1 (1-x^2) (P'n) ^2dx=2n(n+1)/(2n+1)
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124
Integral e^-ax.J(bx) from x=0 to x=infinity =1/√a^2+b^2
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125
prove that L-1{8/(p^2+1)^3}=(3-t^2)sint-3tcost
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126
(D^2+1) y=sinx.sin2x
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127
Solve:xd^2/dx^2-dy/dx-4x^3y=4x^3sinx^2
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128
Solve: p+r+s=1 (Linear Partial Differential Equation with constant coefficients)
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129
Solve by the method of variation of parameters:(1-x)d^2y/dx^2+xdy/dx-y=(1-x)^2
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130
Solve: r+s-6t=ycosx. ||Top mathematics channel on YouTube||#top mathematics channel on YouTube
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131
Solve:x^2(y-z)p+y^2(z-x)q=z^2(x-y)
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132
Solve: p^2+2pycotx-y^2=0 (For solution of this question only watch by video link in description) .
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133
Solve: p+q=x+y+z (Partial differential equation of the first order)Best mathematics channelYouTube
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134
Solve : dx/(y3x-2x^4)=dy/(2y^4-x^3y)=dz/9z(x^3-y3)
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135
Solve:dx/cos(x+y)=dy/sin(x+y)dz/z
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136
Solve: dx/yz=dy/zx=dz/xy
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137
Solve: dx/(mz-ny) =dy/(nx-lz) =dz/(ly-mx)
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138
Solve: xdx/y^2z=dy/xz=dz/y^2
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139
Solve: dx/x^2=dy/y^2=dz/nxy
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140
(x^3D^3-4x^2D^2+5xD-2)y=x^3;D=d/dz Find the general solution of differential equation
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141
Solve : dx/dt+7x-y=0,dy/dt+2x+5y=0
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142
Solve the simultaneous differential equations: d^2/dt^2+3dy/dt+16x=0, d^2y/dt^2-5dx/dt+9y=0.||TOP
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143
Solve: (D^3-3D^2+2)y=x^2.e^x||Top Mathematics channel on YouTube
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144
Solve: xp=1+p^2 ||Top placed mathematics channel on YouTube
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145
Remaining part of (D^2-4D+4)y=e^x.cosx||Top mathematics channel on YouTube
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146
Solve:(D^2-2D-4)y=e^x.cosx||Top mathematics channel on YouTube
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147
Solve: ycos(x/y)dx-{y+xxos(x/y)}dy=0.||Top Mathematics channel on YouTube
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148
Find orthogonal trajectory of the curve r^n.sin4θ=a^n.||Top Mathematics channel on YouTube
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149
Solve:xd^2y/dx^2+(x-2)dy/dx-2y=x^3 ||Top mathematics channel on YouTube
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150
Solve the C. I. of p^2+q^2=x+y ||Top mathematics channel on YouTube||
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151
Solve: xdx/day=2x^2.y ||Top Mathematics channel on YouTube||
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152
Solve: d^2y/dx^2-3dy/dx=2sin3x
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153
Solve: sin2x.dy/dx=y+tanx
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154
Find the equation of the family of curves that is orthogonal to x-4y@=c.Top Mathematics channel
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155
Solve:(D-D')^2z=sinx ||Best mathematics channel on YouTube||Top mathematics channel on YouTube||
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156
Solve:yt-q=xy || Best Mathematics Channel on YouTube || Top Mathematics Channel on YouTube ||
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157
Solve:yzdx/y-z=zxdy/z-x=xydz/x-y ||Top Mathematics Channel on YouTube ||Best Chanel on YouTube||
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158
Solve: (y-z)p+(z-x)q =x-y ||Best Mathematics Channel on YouTube||Top Mathematics Channel on YouTub
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159
Solve: (D^2+a^2)y=xcosnx ||Top Mathematics Channel on YouTube||Best Mathematics channel on YouTube||
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160
Ify=[log(x+√x^2+1)]^2, then prove that (1+x^2)yn+2 +(2n+1)xyn +n^2yn=0||B.Tech.Mathematics||Top Math
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161
If y=[log(x+√x^2+1)]^2, Find (yn) 0.||Top Mathematics Channel on YouTube||Best Mathematics channel |
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162
Solve: p+q=z/a.||Best Mathematics Channel on YouTube||Top Mathematics Channel on YouTube||P.D.E.
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163
Form partial differential equation by eliminating arbitrary constants a, b, and c from z=ax+by+cxy.
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164
x^2ydx-(x^3+y^3)dy=0 ||Top Mathematics channel on YouTube||
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165
Solve: x^2d^2y/dx^2+dy/dx-(1+x^2)y=e^-x ||Unique Solution on You Tube||Best mathematics channel ||
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166
Solve: (x^3+y2+2)dx+2ydy=0 ||Top Mathematics channel on YouTube||Best Mathematics channel on YouTube
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167
d^2x/dt^2+w^2x=0 ||Top Mathematics Channel on YouTube ||
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168
Solve: (D^3+6D^2+11D+6)y=0;D=d/dx ||Top Mathematics Channel on YouTube||Best Mathematics Channel ||
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169
Find the solution of d^2i/dt^2+R/Ldi/dt+1/LCi=0 where R^2C=4L where R, C, L are constants. Top Maths
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170
Solve:(x+y-a/x+y-b)dy/dx=(x+y+a/x+y+b)
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171
Solve: dy/dx+1=e^x-y
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172
Solve: (D^2-D'^2)z=x-y
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173
Solve: (DD'-D'^2)z=x/y^2
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174
solve: costdy/dx+siny.cosy=cosx
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175
(x-y^2)dx+2xydy=0
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176
Solve: (D^2+2DD'+D'^2)z=2cosy-xsiny
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177
Solve: (D^2-1)y =coshxcosx+e^x
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178
Solve: d^4y/dx^4+m^4y=0 or (D^4+m^4)y=0 ||Top Mathematics Channel on YouTube||
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179
Solve: d^2y/dx^2-3dy/dx+2y=e^5x or (D^2-3D+2)y=e^5x
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180
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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181
Solve: (D^2-2D+5)y=e^2xsinx
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182
Find a complete integral of p^3+q^3-3pqz=0.(Partial Differential equation of first order)
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183
Find the complete integral of x^2p^2+y^2q^2=z^2
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184
Solve : xd^2y/dx^2-2(x+1)dy/dx+(x+2)=(x-2)e^x
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185
(D^2-4)y=e^x+sin2x
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186
The general solution of the differential equation x^2d^2y/dx^2+4xdy/dx+2y=e^x is y=c1x^P+c2x^Q+x^e^x
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187
Solve the differential equation by using the method of variation of parameters x^2d^2/dx^2-(x^2+2x)
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188
Solve: d^2y/dx^2-cotxdy/dx-(1-cotx) =e^xsinx
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189
Solve: (p-xy)(p-x^2)(p-y^2)=0
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190
Solve:(D^2-DD'+D'-1)z=cos(x+2y)+e^y
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191
Solve: (D^3+3D-4)y=xe^-2x
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192
Solve: dy/dx=(4x+y+1)^2
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193
Solve: p^2+q^2-2px-2qy+1=0
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194
Solve: r=a^2t
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195
Solve: d^2y/dx^2-y=4xe^x
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196
Find P. I. of (D^2-4DD'+4D'^2+D-2D')z=e^x+y
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197
Solve: d^3y/dx^3+d^2y/dx^2-dy/dx-y=cos2x.
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198
Solve: xd^2y/dx^2-(2x-1)dy/dx+(x-1)y=0
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199
Using method of variation of parameters, solve: (x+2)d^2y/dx^2-(2x+5)dy/+2y=(x+1)e^x.
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200
Solve: d^2y/dx^2-2dy/dx+y=x^2.e^2x
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