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CBSE Questions for Class 12 Commerce Maths Differential Equations Quiz 4 - MCQExams.com

Solution of the given differential equation (1x2)dydx+xy=xy2 is
  • y(1y)=c1x2
  • y(y1)=c1x2
  • x(1x)=c1y2
  • x(x1)=c1y2
Which of the following functions are homogeneous?
  • xsiny+ysinx
  • xey/x+yex/y
  • x2xy
  • arcsin(xy)
Find general solution of  1+4x2dy=y3xdx.
  • 12y2=141+4x2+k
  • 12y2=141+4x2+k
  • 12y2=141+4x2+k
  • 12y2=1414x2+k
The solution of the differential equation (1+cosx)dydx=1cosx is
  • y=tanx2+x+c
  • y=2tanx2x+c
  • y=tanx2x+c
  • y=x2tanx2+c
The equation of the curve in which sub-normal varies as the square of the ordinate is (k is constant of proportionality)
  • y=Ae2kx
  • y=ekx
  • y2/2+kx=A
  • y2+kx2=A
Solve : (tany)dydx=sin(x+y)+sin(xy)
  • secy=2cosx+C
  • secy=2cosx+C
  • secy=cosx+C
  • secy=cosx+C
Find general solution of 2dydx=y(x+1)x.
  • logy2=x+log|x|+k
  • logy2=x+log(x)+k
  • logy=x+log(x)+k
  • 2logy=xlog|x|+k
The solution to the differential equation ylny+xy=0 wherey(1)=e, is:
  • x(lny)=1
  • xy(lny)=1
  • (lny)2=2
  • lny+(x22)y=1
A solution of the differential equation, (dydx)2xdydx+y=0 is
  • y=2
  • y=2x
  • y=2x4
  • y=2x24
The solution to the differential equation (x+1)dydxy=e3x(x+1)2 is
  • y=(x+1)e3x+c
  • 3y=(x+1)+e3x+c
  • 3yx+1=e3x+c
  • ye3x=3(x+1)+c
The solution of dydx=ax+hby+k represent a parabola if:
  • a=2,b=0
  • a=2,b=2
  • a=0,b=2
  • a=0,b=0
The solution of differential equation 
dydx=(y+sinxx) satisfying condition y(0)=1, is
  • cosx=xy1
  • cosx=xy+1
  • cosx=xy
  • cosx=x+1
The solution of the equation d2ydx2=ex+ex is-
Note : (where c & d are arbitrary constants in the given options)
  • y=exex+cx+d
  • y=ex+ex+cx+d
  • y=ex+ex+cx+d
  • None of these
Solution of the differential equation 
(2xy+2)dx+(4x2y1)dy=0 is 
  • 2xy=ce(x+2y)
  • 2x+y=ce(2x+y)
  • x2y=ce(x+2y)
  • 2x+y=ce(x+2y)
Solution of differential equation dxdy=tanx(1+ysinx) is given by -
  • cosecx=y+1+Cey
  • y=tanx+CeX
  • sinxey=1+y+C
  • cosecx=y+Cey
Find the equation of the curve for which the normal at any point (x, y) passes through the origin. The curve represents a :
  • ellipse
  • rectange
  • circle
  • hyperbola
Find general solution of yxdydx=b(1+x2dydx) is:
  • b+kx=y(1+bx)
  • b+ky=x(1+bx)
  • b+ky=x(1+by)
  • b+kx=x(1+by)
Which of the following differential equations has y = x as one of its particular solution?
  • d2ydx2x2dydx+xy=x
  • d2ydx2+xdydx+xy=x
  • d2ydx2x2dydx+xy=0
  • d2ydx2+xdydx+xy=0
Which of the following differential equations has y=c1ex+c2ex as the general solution?
  • d2ydx2+y=0
  • d2ydx2y=0
  • d2ydx2+1=0
  • d2ydx21=0
The solution of the differential equation \dfrac { dy }{ dx } =\dfrac { x-y+3 }{ 2\left( x-y \right) +5 } is
  • 2\left( x-y \right) +\log { \left( x-y \right) } =x+c
  • 2\left( x-y \right) -\log { \left( x-y+2 \right) } =x+c
  • 2\left( x-y \right) +\log { \left( x-y+2 \right) } =x+c
  • None of the above
The general solution of the differential equation \log _{ e }{ \left( \cfrac { dy }{ dx }  \right)  } =x+y is:
  • { e }^{ x }+{ e }^{ -y }=C
  • { e }^{ x }+{ e }^{ y }=C
  • { e }^{ y }+{ e }^{ x }=C
  • { e }^{ -x }+{ e }^{ -y }=C
Find the general solution of dy=y \sec x dx.
  • y=C(\sec x -2\tan x)
  • y=C(\sec x +\tan x)
  • y=C(2\sec x +\tan x)
  • None of these
The solution of the differential equation \dfrac{dx}{x}+\dfrac{dy}{y}=0 is
  • xy=c
  • x+y=c
  • log\, x\, log\, y = c
  • x^2+y^2=c
The general solution of \cfrac{dy}{dx}=\cfrac{2x-y}{x+2y} is
  • {x}^{2}-xy+{y}^{2}=c
  • {x}^{2}-xy-{y}^{2}=c
  • {x}^{2}+xy-{y}^{2}=c
  • {x}^{2}-x{y}^{2}=c
The order and degree of differential equation { \left( 1+3\cfrac { dy }{ dx }  \right)  }^{ 2/3 }=4\cfrac { { d }^{ 3 }y }{ d{ x }^{ 3 } } , are
  • 1,\cfrac{2}{3}
  • 3,1
  • 3,3
  • 1,2
The general solution of the differential equation \dfrac{y\, dx-x\, dy}{y}=0 is:
  • xy = C
  • x = Cy^2
  • y=Cx
  • y=Cx^2
The general solution of the differential equation \displaystyle \frac { dy }{ dx } +\frac { 1+\cos { 2y }  }{ 1-\cos { 2x }  } =0 is given by:
  • \tan { y } +\cot { x } =c
  • \displaystyle \tan { y } -\cot { x } =c
  • \displaystyle \tan { x } -\cot { y } =c
  • \displaystyle \tan { x } +\cot { x } =c
Which of the following are solutions of the differential equation y^{\prime\prime}-y=0 ?
  • y=Ce^x
  • y=C \dfrac {e^x}{2}
  • y=Ce^{-x}
  • None of these
Find a particular solution for the following differential equation.
y'-4y'-12y=te^{4t}
  • y(t)=\dfrac{1}{32}(3t+1)e^{4t}
  • y(t)=-\dfrac{1}{18}(3t+1)e^{4t}
  • y(t)=-\dfrac{1}{36}(3t+1)e^{4t}
  • None of these
If the general solutions of a differential equation is (y+c)^2=cx, where c is an arbitrary constant, then the order and degree of differential equation are:
  • 1,2
  • 2,1
  • 1,1
  • None of these
Which of the following are true?
  • Particular solution is a solution of a differential equation containing no arbitrary constants.
  • Particular Solution is a solution to a differential equation that contains arbitrary, unevaluated constants.
  • General solution is a solution of a differential equation containing no arbitrary constants.
  • General Solution is a solution to a differential equation that contains arbitrary, unevaluated constants.
Verify that y=Cx^3 is a solution of the differential equation xy'-3y=0 for any value of C. Then

find the particular solution determined by the initial condition y=2 when x=-3.
  • y=\dfrac{2}{27}x^2
  • y=-\dfrac{2}{27}x^3
  • y=-\dfrac{2}{25}x^3
  • None of these
The solution for the differential equation \cfrac { dy }{ y } +\cfrac { dx }{ x } =0 is:
  • \cfrac { 1 }{ y } +\cfrac { 1 }{ x } =c
  • \log { x } .\log { y } =c
  • xy=C
  • x+y=c
The solution of differential equation x \dfrac {dy}{dx} + 2y= x^{2} is ____
  • y = \dfrac {x^{2} + C}{4x^{2}}
  • y = \dfrac {x^{2}}{4} + C
  • y = \dfrac {x^{4} + C}{x^{2}}
  • y = \dfrac {x^{4} + C}{4x^{2}}
The solution of the differential equation y\sin\left(\dfrac{x}{y}\right)dx=\left(x \sin\left(\dfrac{x}{y} \right)-y \right) dy satisfying y(\dfrac{\pi}{4})=1 is
  • \cos\dfrac{x}{y}=-\log_ey+\dfrac{1}{\sqrt{2}}
  • \sin\dfrac{x}{y}=\log_ey+\dfrac{1}{\sqrt{2}}
  • \sin\dfrac{x}{y}=\log_ex-\dfrac{1}{\sqrt{2}}
  • \cos\dfrac{x}{y}=-\log_ex-\dfrac{1}{\sqrt{2}}
The integrating factor of linear differential equation \cfrac { dy }{ dx } +y\sec { x } =\tan { x } is:
  • \sec { x } -\tan { x }
  • \sec { x } .\tan { x }
  • \sec { x } +\tan { x }
  • \sec { x } .\cot { x }
The integrating factor of the differential equation \cfrac { dy }{ dx } -y\tan { x } =\cos { x } is:
  • \sec{x}
  • \cos{x}
  • {e}^{\tan{x}}
  • \cot{x}
The solution of \dfrac {d^{2}x}{dy^{2}} - x = k, where k is a non-zero constant, vanishes when y = 0 and tends of finite limit as y tends to infinity, is
  • x = k(1 + e^{-y})
  • x = k(e^{y} + e^{-y} - 2)
  • x = k(e^{-y} - 1)
  • x = k(e^{y} - 1)
For the differential equation { \left( \cfrac { dy }{ dx }  \right)  }^{ 2 }-x\left( \cfrac { dy }{ dx }  \right) +y=0, which one of the following is not its solution?
  • y=x-1
  • 4y={x}^{2}
  • y=x
  • y=-x-1
The solution of the differential equation \dfrac {dy}{dx} = \dfrac {yf'(x) - y^{2}}{f(x)} is:
  • f(x) = y + C
  • f(x) = y(x + C)
  • f(x) = x + C
  • None of the above
Solution of \cfrac { dx }{ dy } +mx=0, m< 0 is
  • x=c{ e }^{ my }
  • x=c{ e }^{ -my }
  • x=my+c
  • x=c
What is the general solution of the differential equation { e }^{ x }\tan { y } dx+\left( 1-{ e }^{ x } \right) \sec ^{ 2 }{ y } dy=0?
  • \sin { y } =c\left( 1-{ e }^{ x } \right) where c is the constant of integration
  • \cos { y } =c\left( 1-{ e }^{ x } \right) where c is the constant of integration
  • \cot { y } =c\left( 1-{ e }^{ x } \right) where c is the constant of integration
  • None of the above
The solution of \dfrac{dy}{dx}=\sqrt{1-x^2-y^2+x^2y^2}  is:
where c is an arbitrary constant
  • {\sin}^{-1}y={\sin}^{-1}x+c
  • 2{\sin}^{-1}y=\sqrt{1-x^2}+{\sin}^{-1}x+c
  • 2{\sin}^{-1}y=x \sqrt{1-x^2}+{\sin}^{-1}x+c
  • 2{\sin}^{-1}y=x \sqrt{1-x^2}+{\cos}^{-1}x+c
What is the general solution of the differential equation {x}^{2}dy+{y}^{2}dx=0?
  • x+y=c where c is the constant of integration
  • xy=c where c is the constant of integration
  • c(x+y)=xy where c is the constant of integration
  • None of the above
What is the solution of \frac{dy}{dx}=2y-1 is :
  • y=\frac{1-e^{-2x}}{2}
  • y=\frac{1+e^{2x}}{2}
  • y=1+e^x
  • y=\frac{1+e^{x}}{2}
What is the number of arbitrary constants in the particular solution of differential equation of third order ? 
  • 0
  • 1
  • 2
  • 3
What is D equal to ?
  • -1
  • 1
  • -2
  • None of the above
What is B equal to ?
  • -1
  • 1
  • 2
  • None of the above
What is the equation of a curve passing through (0, 1) and whose differential equation is given by dy = y tan x dx ? 
  • y = cos x
  • y = sin x
  • y = sec x
  • y = cosec x
What is C equal to ? 
  • 1
  • -1
  • 2
  • None of the above
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