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CBSE Questions for Class 12 Commerce Maths Differential Equations Quiz 7 - MCQExams.com

The general solution of the differential equation exdy+(yex+2x)dx=0 is
  • xex+x2=C
  • xexy2=C
  • yex+x2=C
  • yexx2=C
The solution of differential equation cosx.sinydx+sinx.cosydy=0 is 
  • sinxsiny=c
  • sinx.siny=c
  • sinx+siny=c
  • cosx.cosy=c
Solution of the differential equation: (2xcosy+y2cosx)dx+(2ysinxx2siny)dy=0 is :
  • x2sinx+y2cosx=c
  • x2siny+y2cosx=c
  • x2cosy+y2sinx=c
  • None of these
For the given differential equation find the general solution:
dydx+2y=sinx
  • 15[2sinxcosx]+Ce2x
  • 15[2sinxcosx]+C
  • 12[5sinxcosx]+Ce2x
  • None of these
The differential equation of the system of circles touching the x-axis at origin is  
  • (x2y2)dydx2xy=0
  • (x2+y2)dydx+2xy=0
  • (x2y2)dydx+2xy=0
  • (x2+y2)dydx2xy=0
The solution of xdx+ydy=xdyydxx2+y2 is ________________________.
  • x2+y2=2tan1yx+C
  • x2y2=2tan1yx+C
  • x2+y2=2tan1xy+C
  • x2y2=2tan1xy+C
Solution of differential equation dydx+xsin2y= sinycosyis
  • tany=(x1)+cex
  • coty=(x1)+cex
  • tany=(x1)ex+c
  • coty=(x1)ex+c
Let y=y(x) be the solution of the differential equation sinxdydx+ycosx=4x,x(0,π). If y=(π2)=0,theny(π6) is equal to :
  • 493π2
  • 893π2
  • 89π2
  • 49π2
Let f(x)=cos1(cosx) then 
  • f\left( x \right) is differentable for all xϵR
  • f\left( x \right) is not differentable atxϵ0
  • f\left( x \right) is not differentable ifx=nπ.nϵI
  • f\left( x \right) is not differentable ifx=nπ2nϵI
differential equation of all parabolas whose axis s y - axis.......
  • ydydx+xd2ydx2=1
  • xd2ydx2dydx=1
  • y2dydx+2xdydx=0
  • xdydxx2d2ydx2=0
Letyy(x) be the solution of the differential
equation sinxdydxycosx4x,xϵ(0,π).ify(π2) = 0,
then y (π6) is equal to 
  • 49π2
  • 493π2
  • 893π2
  • None of these
Integrating factors of the differential equation dydx+y=1+yx is 
  • x/ex
  • ex/x
  • xex
  • ex
Solution of differential equation dydx+yx=1(1+nx+ny) is (where C is an integration constant)
  • 2(1+n(xy))=x2+C
  • xyn(xy)=x2+C
  • (1+n(xy))=x2+C
  • 2xyn(xy)=x2+C
The solution of the differential equation (x2yx2)y3x=k+y2+xy2=0 is?
  • log(xy)=1x+1y+c
  • log(yx)=1x+1y+c
  • log(xy)=1x+1y+c
  • log(xy)+1x+1y=c
An integrating factor for the DE:(1+y2)dx(tan1yx)dy=0 is 
  • tan1y
  • etan1y
  • 11+y2
  • 1x(1+y2)
Solution of differential equation (2y+xy3)dx+(x+x2y2)dy=0
  • xy2+x3y33=c
  • xy2x3y33=c
  • x2y+x4y43=c
  • None of these
Solution of the differential equation (x2+1)y+2xy=4x2 is 
  • y(1+x2)=4x33+C
  • y(1x2)=x3+C
  • y(1x2)=x32+C
  • None of these
Consider the differential equation, ydx(x+y2)dy=0. If for y=1, x takes value 1, then value of x when y=4 is:

  • 16
  • 36
  • 64
  • 9
General solution of the differential equation dydx=1+xy is
  • y=cex2/2
  • y=cex2/2
  • y=(x+c)ex2/2
  • None
The solution of the differentiable equation x2dydx.cos1xysin1x=1, where y1 as x is
  • y=sin1xcos1x
  • y=x+1xsin1x
  • y=cos1xsin1x
  • y=x+1xcos1x
The population  p(t)  at time  t  of a certain mouse species satisfies the differential equation  dp(t)dt=0.5p(t)450.  If  p(0)=850,  then the time at which the population becomes zero is
  • 12ln18
  • ln18
  • 2ln18
  • ln9
The solution of differential equation  cos2xdydx(tan2x)y=cos4x,|x|<π4,  where y(π6)=338
  • y=tan2xcos2x
  • y=cot2xcos2x
  • 2y=tan2xcos2x
  • 2y=cot2xcos2x
The order of the differential equation
2x2d2ydx23dydx+y=0 is
  • 2
  • 1
  • 0
  • Not defined
The general solution of the differential equation ydxxdyy=0 is
  • xy=C
  • x=Cy2
  • y=Cx
  • y=Cx2
A differential equation associated with the primitive y=a+b e5x+c e7x is
  • y3+2y2y1=0
  • y3+2y235y1=0
  • 4y3+5y220y1=0
  • none of these
If υμ+μυ=6, then dυdμ=
  • 17μυμ17υ
  • μ17υ17μυ
  • 17μ+υμ17υ
  • μ+17υ17μυ
The number of arbitrary constant in the particular solution of a differential equation is
  • 3
  • 4
  • infinite
  • zero
Solution of differential equation siny.dydx+1xcosy=x4cos2y is
  • xsecy=x6+C
  • 6xsecy=x+C
  • 6xsecy=x6+C
  • 6xsecy=6x6+C
The general solution of the differential equation dydx=ex+y  is : 
  • ex+ey=c
  • ex+ey=c
  • ex+ey=c
  • ex+ey=c
The solution of the differential equation 2x2ydydx=tan(x2y2)2xy2 given y(1)=π2 is
  • sin (x2y2)1=0
  • cos(π2+x2y2)+x=0
  • sin(x2y2)=ex1
  • sin(x2y2)=e2(x1)
The solution of the equation (x2+xy)dy=(x2+y2)dxis 
  • logx=(xy)+yx+c
  • logx=2log(xy)+yx+c
  • logx=log(xy)+xy+c
  • none of these above
Solve the given differential equation dydx=(cosxsinx),
  • y=sinx+cosx+c
  • y=sinxcosx+c
  • y=tanx+secx
  • None  of  these
The solution of the differential equation xdydx=y(logylogx+1) is
  • y=xecx
  • y+xecx=0
  • y+ex
  • none of these
Which of the following functions is differentiable at x=0?
  • e|x||x|
  • e|x|+|x|
  • |x|e|x|
  • |x|e|x|
Solution of the differential equation of (y2x3)dxxydy=0 is
  • y2+2x3+cx2=0
  • y22x3+cx2=0
  • y2+2x3cx2=0
  • y2+3x3+cx2=0
The integrating factor (I.F) of differential equation dydx(1+x)xy=1x is _____
  • (1+x)ex
  • (x1)ex
  • (1+x)ex
  • (1x)ex
If cosxdydxysinx=6x,(0<x<π2) and y(π3)=0 then y(π6) is equal to:
  • π243
  • π22
  • π223
  • π223
Let f(x) be a function such that f(0)=f(0)=0,f(x)=sec4x+4, then the function is
  • log(sinx)+13tan3x+xb
  • 23log(sec2x)+16tan2x+2x2
  • log(cosx)+16cos2x+x25
  • None of these
if y=y(x) and 2+sinxy+1(dydx)=cosx,y(0)=1,theny(π/2) equals
  • 1/3
  • 2/3
  • -1/3
  • 1
If xdydx=y(logylogx+1), then the solution of the equation is 
  • logxy=cy
  • logyx=cy
  • logxy=cx
  • None of these
Solution of dydx+2xy=y is 
  • y=cexx2
  • y=cex2x
  • y=cex
  • y=cex2
The solution of differential equation yy=x(y2x2+f(y2/x2)f(y2/x2)) is
  • f(y2/x2)=cx2
  • x2f(y2/x2)=c2y2
  • x2f(y2/x2)=c
  • f(y2/x2)=cy/x
The solution of dvdt+kmv=g is
  • v=cekmtmgk
  • v=cmgkekmt
  • vekmt=cmgk
  • vekmt=cmgk
The solution of the equation (x2y+x2)dx+y2(x1)dy=0 is given by
  • x2+y2+2(xy)+2ln(x1)(y+1)c=0
  • x2+y2+2(xy)+ln(x1)(y+1)c=0
  • x2+y2+2(xy)2ln(x1)(y+1)c=0
  • None of these
Solution of 2ysinxdvdx=2sinxcosxy2cosx, for x=π2,y=1 is 
  • y2=sinx
  • y=sin2x
  • y2=1+cosx
  • None of these
If ϕ(x)={ϕ(x)}2dx and ϕ(1)=0 then ϕ(x)=
  • {2(x1)}1/4
  • {5(x2)}1/5
  • {3(x1)}1/3
  • None of these
Solution of differential equation dysinxsinydx=0 is
  • ecosxtany2=c
  • ecosxtany=c
  • cosxtany=c
  • cosxsiny=c
if integrating factor of x(1x2)dy+(2x2yyax3)dx=0 is epdx, then P is equal to 
  • 2x2ax3x(1x2)
  • 2x31
  • 2x2aax3
  • 2x21x(1x2)
The solution of differentiation equation (2y+xy3)dx+(x+x2y2)dy=o is 
  • x2y+x3y33=c
  • xy2+x3y33=c
  • x2y+x4y44=c
  • None of these
The solution of differential equation x+ydydxyxdydx=xcos2(x2+y2)y3 is
  • tan(x2+y2)=x2y2+c
  • cot(x2+y2)=x2y2+c
  • tan(x2+y2)=y2x2+c
  • tan(x2+y2)=y2x2+c
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Practice Class 12 Commerce Maths Quiz Questions and Answers