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CBSE Questions for Class 12 Commerce Maths Differential Equations Quiz 6 - MCQExams.com

If y=cos1x then (1x2)yxy=? where y=dydx
  • 1
  • 0
  • 2x
  • 2y
Solution of y2dx+(x2xy+y2)dy=0 
  • tan1(xy)+logy+c=0
  • 2tan1(xy)+logy+c=0
  • logy(y+x2+y2)+logy+c=0
  • logy(yx2+y2)+logy+c=0
If y=1x1+x then find (1x2)dydx+y =
  • 1
  • 1
  • 2
  • 0

If tangent at point p, with parameter t, on the curve x=4t2+3,y=8t31,tϵR, meets the curve again at point Q, then the coordinates of Q are:- 

  • t2+3,-t31
  • 4t2+3,8t21
  • t2+3,t31
  • 16t2+3,64t31
The solution of xdydx+ylogy=xyex is 
  • logy=(x1)ex+c
  • (x1)logy=xex+c
  • xlogy=(x+1)ex+c
  • xlogy=(x1)ex+c
The real value of n for which substitution y=un will transform differential equation 2x4ydydx+y4=4x6 into homogeneous equation
  • 12
  • 1
  • 32
  • 4
The solution of the differential equation xdydx=y+xtanyx is :
  • sinxy=cx
  • sinyx=cx
  • sinxy=cy
  • sinyx=cy
Soluation of D.E. dydx=3x+4y+312x+16y4 is 
  • y=4x+n|3x+4y|+C
  • 4y=x+n|3x+4y|+C
  • y=n|3x+4y|+C
  • x+y=n|3x+4y|+C
Solution of the differential equation tanysec2xdx+tanxsec2ydy=0 is:
  • tanx+tany=k
  • tanxtany=k
  • tanxtany=k
  • tanx.tany=k
The solution of the differential equation ydx+(x+x2y)dy=0 is-
  • 1xy+logy=c
  • logy=cx
  • 1xy=c
  • 1xy+logy=c
The general solution of the differential equation dydx+ycotx=cscx, is
  • x+ysinx=C
  • x+ycosx=C
  • y+x(sinx+cosx)
  • ysinx=x+C
The solution of dydx=(ax+bcy+d) represents a parabola if:- 
  • a=0,c=0
  • a=1,c=2
  • a=0,c0
  • a=1,c=1
The solution of the differential equation xdx+ydy=x2ydyy2xdx is
  • x21=C(1+y2)
  • x2+1=C(1y2)
  • x31=C(1+y3)
  • x3+1=C(1y3)
Solve differential equation dx=xdvv2a2.
  • x2a=vav+a×c
  • x2a=v+ava×c
  • x=vav+a×c
  • None of these
Solution for x+ydydxyxdydx=x2+2y2+y4x2 is 
  • yx1x2+y2=c
  • yx+1x2y2=c
  • xy+1x2+y2=c
  • xy1x2+y2=c
The particular solution of the differential equation y(1+logx)dxdyx=0 when x=e,y=e2 is
  • y=exlogx
  • ey=xlogx
  • xy=elogx
  • ylogx=ex
Solution of differential equation xdyyx=0 represents:
  • rectangular hyperbola
  • straight line passing through origin
  • parabola whose vertex is at origin
  • circle whose center is at origin
The solution of cosylog(secx+tanx)dx=cosxlog(secy+tany)dy is 
  • [log(secx+tanx)]2[log(secy+tany)]2=c
  • [log(secx+tanx)]2+[log(secy+tany)]2=c
  • [log(secxtanx)]2[log(secytany)]2=c
  • [log(secxtanx)]2+[log(secytany)]2=c
The solution of dydx=xlog x2+xsiny+ycosy
  • ysiny=x2logx+c
  • ysiny=x2+c
  • ysiny=x2+logx+c
  • ysiny=xlogx+c
The solution to the differential equation cos xdy=y(sinxy)dx, 0<x<π2, is
  • tanx=(secx+c)y
  • secx=(tanx+c)y
  • ysecx=tanx+c
  • ytanx=secx+c
The solution of dydx=yx+tan(yx).
  • sin(yx)=cx
  • sin(yx)=cy
  • cos(yx)=cx
  •  sec(yx)+tan(yx)=xc 
If c is any arbitrary constant, then the general solution  of differential equation ydxxdy=xydx is  given by -
  • y=cxex
  • y=cxex
  • y+ex=cx
  • yex=cx
Solve :

(xx)x(2xlogex+x)dx 
  • x(xx)+C
  • (xx)x+C
  • xxlogex+C
  • (xx)+C
The solution of the equation dydx+1y21x2=0 is 
  • x1y2y1x2=c
  • x1y2+y1x2=c
  • x1+y2+y1+x2=c
  • None of these
The solution of dydx=x2y2+yx.
  • tan1(yx)=log(cx)
  • sin1(yx)=log(cx)
  • cos1(yx)=log(cy)
  • sec1yx=log(cy)
The solution of the differential equations dydx=x2y+12x4y is?
  • (x2y)2+2x=c
  • (x2y)2+x=c
  • (x2y)+2x2=c
  • (x2y)+x2=c
The solution of x1+y2dx+y1+x2dy=0.
  • sinh1x+sinh1y=c
  • 1+x2+1+y2=c
  • (1+x2)(1+y2)=c
  • 1+x21+y2=c
The solution of dydx=(1+y2)(1+x2)1 is?
  • yx=c(1+xy)
  • y+x=c(1+xy)
  • y=(1+2x)c
  • xy=x2+x+x
The solution of dydx=y2xyx2.
  • y=cexy
  • y=eyxc
  • logy=xy+c
  • logx=xy+c
If f:RR be a continuous   function such that f(x)=x12tf(t)dt, then which of the following does not hold(s) good?
  • f(π)=eπ2
  • f(1)=e
  • f(0)=1
  • f(2)=2
The solution of the differential equation x2dy=2xydx is
  • xy2=c
  • x2y2=c
  • x2y=c
  • xy=c
Solution of the differential equation dydx+ysecx=tanx(x<π2) is 
  • y(secxtanx)=(secx+tanx)x+C
  • y(secx+tanx)=(secxtanx)x+C
  • y(secx+tanx)=(secx+tanx)x+C
  • noneofthese
Solution of the differential equation xdyydx=x2+y2dx is
  • y+x2+y2=cx
  • y+x2+y2=cx2
  • y+x2+y2=C
  • none of these
The solution of the differential equation dydx=1+x+y+xy is
  • log(1+y)=x+x22+c
  • (1+y)2=x+x22+c
  • log(1+y)=log(1+x)+c
  • None of these
A continuously differentiable function ϕ(x) in (0,π) satisfying y=1+y2,y(0)=0=y(π) is
  • tanx
  • x(xπ)
  • (xπ)(1ex)
  • Not possible
Solution of the differential equation (1+x2)dy+2xydx=cotxdx is
  • y=log|sinx|(1+x2)+C(1+x2)1
  • y=log|sinx|(1+x2)1+C(1+x2)
  • y=log|sinx|(1+x2)+C(1+x)
  • y=log|sinx|(1+x2)1+C(1+x2)1
The solution of the differential equation x3dydx+4x2tany=exsecy satisfying y(1)=0 is 
  • tany=(x2)exlogx
  • siny=ex(x1)x4
  • tany=(x1)exx3
  • siny=ex(x1)x3
The solution of dydx=1+y2secx is
  • tan1y=cosx+c
  • tan1y=sinx+c
  • y3=cosecx+c
  • log(1+y2)=cosx+c
The solution of ydxxdy=0 is
  • y2=cx
  • y=cx3
  • y=cx
  • x2=cy
Solution of differential equation dydx2xy=x is
  • y=Cex212
  • y=Cex2+12
  • y=Cx212
  • None
If 2x=y15+y15and(x21)d2ydx2+λxdydx+ky=0,thenλ+K is equal to.
  • 26
  • -24
  • -23
  • -26
The solution of ydxxdy+3x2y2ex3dx=0
  • xy+ex3=c
  • xyex3=c
  • xy=ex3+c
  • none of these
The solution of, xdyx2+y2=(yx2+y21)dx, is given by
  • tan1(xy)+x=C
  • tan1(yx)+x=C
  • tan1(yx)+xy=C
  • tan1(yx)+x2=C
The solution of the differential equation xdy(y2exy+exy)=ydx(exyy2exy) is-
  • xy=ln|ex/y+C|
  • exy=ln(xy+C)
  • xy=ex/y+C
  • xy=ex/y+xy
The solution of the differential equation (xcoty+logcosx)dy +(logsinyytanx)dx=0 is:-
  • (sinx)y(cosy)x=c
  • (siny)x(cosx)y=c
  • (sinx)x(cosy)y=c
  • none of these
The solution of the differential equation y2dy=x(ydxxdy) is y=y(x). If y(3e)=e and y(x0)=1 then x0 is
  • 0
  • 1
  • 1e
  • 1
The differential equation whose solution is y=Ax5+Bx4 is
  • x2d2ydx2+8xdydx+20y=0
  • x2d2ydx2+8xdydx20y=0
  • x2d2ydx28xdydx+20y=0
  • x2d2ydx28xdydx20y=0
Solution of the equation dydx=1+xy+x+y is
  • (1+y)(1+x)=c
  • log(1+y)=1+x+c
  • ln|1+y|=x+x22+c
  • ln|1+y|+x+x22+c=0
The general solution of the differential equation dydx+y=x3 is ______.
  • yex=ex(x3+3x26x6)+c
  • yex=ex(x33x26x+6)+c
  • y=(x33x2+6x6)+cex
  • y=ex
If dydx=y+3>0 and y(0)=2 then y(ln2) is equal to :
  • 7
  • 5
  • 13
  • 2
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