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CBSE Questions for Class 12 Commerce Maths Differential Equations Quiz 10 - MCQExams.com

Solution of the differential equation {1xy2(xy)2}dy+{y2(xy)21y}dx=0  is
  • ln|xy|+xyxy=c
  • xyxy=cex/y
  • ln|xy|=c+xyxy
  • none of these
The solution of the differential equation x2dydxcos(1x)ysin(1x)=1;where y1 as x is 
  • y=sin(1x)cos(1x)
  • y=x+1xsin(1x)
  • y=cos(1x)+sin(1x)
  • y=x+1xcos(1x)
The solution of the differential equation dydx=x2+y2+12xy satisfying y(1)=1, is
  • a hyperbola
  • a circle
  • y2=x(1+x)10
  • (x2)2+(y3)2=5
The general solution of differential equation dydx=sin3xcos2x+xex
  • y=15cos5x+13csc3x+(x+1)ex+c
  • y=15cos5x13csc3x+(x1)ex+c
  • y=15cos5x13csc3x(x1)exc
  • None of these
The value of limx y(x) obtained from the differential equation dydx=yy2, where y(0) = 2 is 
  • 1
  • -1
  • 0
  • 22e
The solution of the differential equation dydx+1xtany=tanysinyx2 is 
  • 1xcosy=12x2+K
  • 1xcoty=12x2+K
  • 1xcscy=12x2+K
  • 1xcosx=12x2+K
The solution of the differential equation (3xy+y2)dx+(x2+xy)dy=0 is
  • x2(2x+y)=3
  • y2(2x+y)=3
  • x2y(2x+y)=3
  • x2y(2x+3)=9
The solution of the differential equation (x2+1)dydx+y2+1=0, is  [ify(0)=1]
  • y=2+x2
  • y=(1+x)(1x)
  • y=x(x1)
  • y=(1x)(1+x)
The solution of differential equation dydx=x(2lnx+1)siny+ycosy is
  • ysiny=xlnx+c
  • ysiny=x2lnx+c
  • siny=x2lnx+c
  • ycosy=x2lnx+c
The equation of a curve passing through the point (0, 0) and whose differential equation is y=exsinx is 
  • 2y1=ex(sinxcosx)
  • 2y1=ex(cosxsinx)
  • 2y+1=ex(cosxsinx)
  • Noneofthese
Solution of the differential equation ye^{x/y}dx=(xe^{\frac {x}{y}}+y^{2})dy(y \neq 0) is ?
  • e^{x/y}=x+C
  • e^{x/y}+x=C
  • e^{y/x}=x+C
  • e^{x/y}=y+C
Solution of differential equation xdy=(y-{x}^{2}-{y}^{2})dx is (where c is arbitrary constant)
  • y=x\cos{(c+x)}
  • y=x\tan{(x-c)}
  • y=x\csc{(c+x)}
  • none of these
Let y=y(x) be the solution of the differential equation (1-x^2)\dfrac{dy}{dx}-xy=1,x\in(-1,1) if y(0)=0, then y\left(\dfrac{1}{2}\right) is equal to
  • \dfrac{\pi}{3\sqrt3}
  • \dfrac{\pi}{\sqrt3}
  • \dfrac{\pi}{6}
  • \dfrac{\pi}{3}
If the general solution of the differential equation if y'=\frac { y }{ x } +\Phi \left( \frac { x }{ y }  \right) , for some function \Phi , is given by yin|cx|=x, where c is an arbitrary constant, then \Phi (2) is equal to :
  • 4
  • \frac { 1 }{ 4 }
  • -4
  • -\frac { 1 }{ 4 }
(2y+xy^{3})dx+(x+x^{2}y^{2})dy=0 solution of differential equation is 
  • 3x^{2}y+x^{3}y^{2}=c
  • 3x^{2}y^{2}+xy^{2}=c
  • yx^{2}+\dfrac{xy}{3}=c
  • x^{2}y+\dfrac{x^{3}y^{3}}{3}=c
Solution of differential equation { x }^{ 6 }dy+3{ x }^{ 5 }ydx=xdy-2y\ dx is
  • { x }^{ 3 }y=\dfrac { y }{ { x }^{ 2 } } +C
  • { x }^{ 3 }y=\dfrac { 2y }{ { x }^{ 2 } } +C
  • { x }^{ 3 }{ y }^{ 2 }=\dfrac { y }{ { x }^{ 2 } } +C
  • { x }^{ 3 }=\dfrac { y }{ { x }^{ 2 } } +C
The solution of equation \dfrac { dy }{ dx } =\dfrac { 1 }{ x+y+1 }
  • x={ ce }^{ y }-y-2
  • y=x+{ ce }^{ y }-2
  • x+{ ce }^{ y }-2-2=0
  • y=x
Let y=y(x) be the solution of the differential equation \sin x\dfrac {dy}{dx}+y\cos x=4x,x\ \in\ (0,\pi), if y\left(\dfrac {\pi}{2}\right)=0, then y\left(\dfrac {\pi}{6}\right) is equal to
  • -\dfrac {4}{9}\pi^{2}
  • \dfrac {4}{9\sqrt {2}}\pi^{2}
  • \dfrac {-8}{9\sqrt {2}}\pi^{2}
  • -\dfrac {8}{9}\pi^{2}
Solution of the differential equation dr=a\left( r\sin\theta d\theta-\cos\theta dr \right ) is 
  • r\left( 1+a\cos { \theta } \right) =c
  • r\left( 1+a\cos { \theta } \right) =ac
  • r\left( 1-a\cos { \theta } \right) =c
  • r\left( 1-a\cos { \theta } \right) =ac
The solutions of the differential equation  \frac{dy}{dx}= \frac{siny+x}{sin2y-x cos y } is 

  • sin^{2}y = xsin y +\frac{x^{2}}{2}+c
  • sin^{2}y = xsin y -\frac{x^{2}}{2}+c
  • sin^{2}y = x+sin y +\frac{x^{2}}{2}+c
  • sin^{2}y = x-sin y +\frac{x^{2}}{2}+c
The general solution of the differential equation \dfrac{dy}{dx} + \sin \dfrac{x+y}{2} = \sin \dfrac{x-y}{2} is
  • \log \left(\tan \dfrac{y}{2}\right) = c-2\sin x
  • \log\left( \tan \dfrac{y}{4}\right) = c-2\sin \left(\dfrac{x}{2}\right)
  • \log \left(\tan \left(\dfrac{y}{2} +\dfrac{\pi}{4}\right) \right)= c-2 \sin x
  • None of the above
If y\left(x\right) is the solution of the differential equation \left(x+2\right)\dfrac{dy}{dx}=x^{2}+4x-9,x\neq -2 and y\left(0\right)=0, then y\left(-4\right) is equal to 
  • 0
  • 1
  • -1
  • 2
The solution of differential equation,\left(x+\tan y\right)dy=\sin 2y\,dx is
  • xcoty=\dfrac{1}{2}\log |cosec2y-cot2y|+c
  • x=\tan y+c\sqrt{\tan y}
  • x=\cot y+c\sqrt{\cot y}
  • None\ of\ these
If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation, y(1+xy)dx=xdy, then f\left(-\dfrac {1}{2}\right) is equal to
  • -\dfrac {4}{5}
  • \dfrac {2}{5}
  • \dfrac {4}{5}
  • -\dfrac {2}{5}
General solution of differential equation x^{2}(x+y\frac{dy}{dx})+(x\frac{dy}{dx}-y)\sqrt{x^{2}+y^{2}}=0 is
  • \frac{1}{\sqrt{x^{2}+y^{2}}}+\frac{y}{x}=c
  • \sqrt{x^{2}+y^{2}}-\frac{y}{x}=c
  • \sqrt{x^{2}+y^{2}}+\frac{y}{x}=c
  • 2\sqrt{x^{2}+y^{2}}+\frac{y}{x}=c
  • \frac{1}{\sqrt{x^{2}+y^{2}}}-\frac{y}{x}=c
Solution of the differential equation \dfrac{dy}{dx}=\dfrac{y(1+x)}{x(y-1)} is
  • \log|xy|+x-y=C
  • \log|xy|-x+y=C
  • \log|xy|+x+y=C
  • \log|xy|-x-y=C
Solution of (x+y-1)dx+(2x+2y-3)dy=0 is 
  • y+x+log(x+y-2)=c
  • y+2x+log(x+y-2)=c
  • 2y+x+log(x+y-2)=c
  • 2y+2x+log(x+y-2)=c
The solution of \dfrac{xdy}{x^{2}+y^{2}}=\left(\dfrac{y}{x^{2}+y^{2}}-1\right)dx is 
  • y=x\cot(c-x)
  • \cos^{-1}u/x=-x+C
  • y=x\tan (c-x)
  • y^{2}/x^{2}=x\tan (c-x)
General solution of differential equation x^2dy + y(x + y)dx = 0 is 
  • 2x + y = Ax^2Y
  • 2x - y = \dfrac{Ax^2}{y}
  • 2x + y = \dfrac{Ax^2}{y}
  • x - 2y = Ax^2y
If y(t) is solution of (t + 1) \dfrac{dy}{dt} - ty = 1, y(0) = -1, then y(1) =
  • \dfrac{1}{4}
  • -2
  • -\dfrac{1}{2}
  • \dfrac{1}{2}
Solution of the differential equation \cos{\,}x {\,}dy=y(\sin{\,}x-y)dx,0<x<\dfrac{\pi}{2} is
  • y sec x= tan x + c
  • y sec x= sec x + c
  • y sec x= (sec x + c) y
  •  sec x= y (tan x + c) 
The solution of the differential equation ydx-xdy+3x^2y^2e^{x^3} dx=0 is
  • \dfrac{x}{y}+e^{x^3}=c
  • \dfrac{x}{y}-e^x=c
  • \dfrac{x}{y}+ex^{x^3}-x^2y=c
  • \dfrac{x}{y}-e^{x^3}=c
Solution of the equation (x+y)^2\dfrac{dy}{dx}=4,y(0)=0 is
  • y=2tan^{-1}\left(\dfrac{x+y}{2}\right)
  • y=4tan^{-1}\left(\dfrac{x+y}{4}\right)
  • y=4tan^{-1}\left(\dfrac{x+y}{2}\right)
  • y=2tan^{-1}\left(\dfrac{x+y}{4}\right)
The solution of the differential equation \log\left(\dfrac {dy}{dx}\right)=4x-2y-2,y=1 when x=1 is
  • 2e^{2y+2}=e^{4x}+e^{2}
  • 2e^{2y-2}=e^{4x}+e^{2}
  • 2e^{2y+2}=e^{4x}+e^{4}
  • 3e^{2y+2}=e^{3x}+e^{2}
the solution of ydx-xdy+3{ x }^{ 2 }{ y }^{ 2 }{ e }^{ { x }^{ 3 } }dx=0 is
  • \frac { x }{ y } +{ e }^{ { x }^{ 3 } }=C
  • \frac { x }{ y } -{ e }^{ { x }^{ 3 } }=0
  • -\frac { x }{ y } +{ e }^{ { x }^{ 3 } }=C
  • none of these
The solution of the differential equation \left(x+2y^{3}\right)\dfrac{dy}{dx}=y is 
  • \dfrac{x}{y^{2}}=y+C
  • \dfrac{x}{y}=y^{2}+C
  • \dfrac{x^{2}}{y}=y^{2}+C
  • \dfrac{x}{y}=x^{2}+C
General solution of the differential equation (x+y-2) dy=(x+y) dx is 
  • y+x=log(y-x+1)+c
  • y-x log (x+y-1)+c
  • y-2x=log (x+y-1)+c
  • y+2x=log (x+y+1)+c
The solution of x^2dy-y^2dx+xy^2(x-y)dy=0 is?
  • ln\left|\dfrac{x-y}{xy}\right|=\dfrac{y^2}{2}+c
  • ln\left|\dfrac{xy}{x-y}\right|=\dfrac{x^2}{2}+c
  • ln\left|\dfrac{x-y}{xy}\right|=\dfrac{x^2}{2}+c
  • ln\left|\dfrac{x-y}{xy}\right|=x+c
Solution of \left(1+xy\right)ydx+\left(1-xy\right)xdy=0 is 
  • \log\dfrac{x}{y}+\dfrac{1}{xy}=c
  • \log\dfrac{x}{y}=c
  • \log\dfrac{x}{y}-\dfrac{1}{xy}=c
  • \log\dfrac{y}{x}-\dfrac{1}{xy}=c
The general solution of the differential equation y-x\dfrac{dy}{dx}=y^{2}\cos x\left(1-\sin x\right) is
  • y\left(\sin x+c\right)=\tan x+\sec x
  • y\left(\sin x+c\right)=\tan x-\sec x
  • \dfrac{x}{y}=\sin x+\dfrac{1}{4}\cos 2x+c
  • \dfrac{x}{y}=\sin x+\dfrac{1}{8}\cos 2x+c
Solution of  \dfrac { d y } { d x } + 2 x y = y  is
  • y = c e ^ { x - x ^ { 2 } }
  • y = c e ^ { x ^ { 2 } } - x
  • y = c e ^ { x }
  • y = c e ^ { - x ^ { 2 } }
Let =y(x) be the solution of the differential equation, x\frac { dy }{ dx } +y=x{ log }_{ e }x,(x>1). If 2y(2)={ log }_{ e }4-1, then y(e) is equal to :
  • -\dfrac { { e }^{ 2 } }{ 2 }
  • \dfrac  { e } { 4 }
  • \dfrac { { e }^{ 2 } }{ 4 }
  • -\dfrac { { e }^{ 2 } }{ 4}
The solution of the Differential Equation (x+y)(dx-dy)=dx+dy is
  • l\ n(x-y)=x+y+C
  • l\ n(x+y)=x-y+C
  • l\ n(x-y)=x-y-C
  • none\ of\ these
The integrating factor of the equation y^{2}dx+(3xy-1)dy=0 is
  • y^{2}
  • y^{3}
  • \dfrac {1}{y^{2}}
  • \dfrac {1}{y^{3}}
The solution of the differential equation \dfrac{dy}{dx}=\sec (x+y) is 
  • y-\tan\dfrac{x+y}{2}=c
  • y+\tan\dfrac{x+y}{2}=c
  • y+2\tan\dfrac{x+y}{2}=c
  • None\ of\ these
The solution of differential equation dy/dx -y/x+\tan y/x is:
  • x=C'\cos (y/x)
  • x=C'\sin (y/x)
  • x=C'\csc (y/x)
  • none\ of\ these
The solution of the equation \dfrac{dy}{dx}=\dfrac{(1+x)y}{(y-1)x} is:
  • \log xy+x+y=c
  • \log (\dfrac{x}{y})+x-y=c
  • y-x-\log xy=c
  • None\ of\ these
Solution of \left(\dfrac {dy}{dx}\right)^{2}+x\dfrac {dy}{dx}-y=0 is
  • y=3x^{2}+9
  • y=3x+9
  • y=\dfrac {4}{3}x^{2}
  • y=9x+3
Number of values of m \in N, for which y=e^{mx} is a solution of the differential equation D^3y-3D^2y-4Dy+12y=0, is?
  • 0
  • 1
  • 2
  • More than 2
The solution the differential equation \left(\dfrac{dy}{dx}\right)^{2}-\dfrac{dt}{dx}(e^{x}+e^{-x})+1=0 is/are 
  • y+e^{-x}=c
  • y-e^{-x}=c
  • y+e^{x}=c
  • y-e^{x}=c
0:0:2


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