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CBSE Questions for Class 12 Commerce Maths Differential Equations Quiz 5 - MCQExams.com

The solution of dydx=|x| is :
  • y=x|x|2+c
  • y=|x|2+c
  • y=x22+c
  • y=x32+c
The solution of the differential equation dydx=exy(exey) is
  • ey=(ex+1)+Ceex
  • ey=(ex1)+C
  • ey=(ex1)+Ceex
  • None of the above
The solution of the differential equation \dfrac {dy}{dx} = \tan \left (\dfrac {y}{x}\right ) + \dfrac {y}{x} is:
  • \cos \left (\dfrac {y}{x}\right ) = cx
  • \sin \left (\dfrac {y}{x}\right ) = cx
  • \cos \left (\dfrac {y}{x}\right ) = cy
  • \sin \left (\dfrac {y}{x}\right ) = cy
The solution of the differential equation \displaystyle (x^2-yx^2)\frac{dy}{dx}+y^2+xy^2=0 is?
  • \displaystyle \log\left(\frac{x}{y}\right)=\frac{1}{x}+\frac{1}{y}+C
  • \displaystyle \log\left(\frac{y}{x}\right)=\frac{1}{x}+\frac{1}{y}+C
  • \displaystyle \log(xy)=\frac{1}{x}+\frac{1}{y}+C
  • \displaystyle \log(xy)+\frac{1}{x}+\frac{1}{y}=C
The solution of \dfrac{dy}{dx} = 1+y+y^2+x+xy+xy^2 is
  • \tan^{-1}\left(\dfrac{2y+1}{\sqrt{3}}\right) = x+x^2+C
  • 4\tan^{-1}\left(\dfrac{2y+1}{\sqrt{3}}\right) = \sqrt{3}(2x+x^2)+C
  • \sqrt{3}\tan^{-1}\left(\dfrac{3y+1}{3}\right)=4(1+x+x^2)+C
  • \tan^{-1}\left(\dfrac{2y+1}{3}\right)=4(2x+x^2)+C
The solution of the differential equation \sec^{2} x \cdot \tan y \,dx + \sec^{2} y \cdot \tan x\ dy = 0 is 
  • \tan x \cdot \cot y = C
  • \cot x \cdot \tan y = C
  • \tan x \cdot \tan y = C
  • \sin x \cdot \cos y = C
The solution of the differential equation \dfrac {dy}{dx} = (x + y)^{2} is:
  • \dfrac {1}{x + y} = c
  • \sin^{-1} (x + y) = x + c
  • \tan^{-1} (x + y) = c
  • \tan^{-1} (x + y) = x + c
The solution of the differential equation (1+{ x }^{ 2 }{ y }^{ 2 })ydx+({ x }^{ 2 }{ y }^{ 2 }-1)xdy=0 is
  • xy=\log { \dfrac { x }{ y } } +C
  • xy=2\log { \dfrac { y }{ x } } +C
  • {x}^{2}{y}^{2}=\log { \dfrac { y }{ x } } +C
  • {x}^{2}{y}^{2}=2\log { \dfrac { y }{ x } } +C
What is the curve which passes through the point (1, 1) and whose slope is \dfrac{2y}{x} ?
  • Circle
  • Parabola
  • Ellipse
  • Hyperbola
If x  dy = y  dx + y^2 dy, y > 0 and y(1) = 1, then what is y(-3) equal to?
  • 3 only
  • -1 only
  • Both -1 and 3
  • Neither -1 nor 3
Solution of the differential equation \dfrac { dx }{ x } +\dfrac { dy }{ y } =0 is
  • \dfrac { 1 }{ x } + \dfrac { 1 }{ y } =c
  • \log { x } \log { y } =c
  • xy=c
  • x+y=c
A solution of the differential equation { \left( \dfrac { dy }{ dx }  \right)  }^{ 2 }-x\dfrac { dy }{ dx } +y=0 is
  • y=2
  • y=2x
  • y=2x-4
  • y=2{ x }^{ 2 }-4
The solution of the differential equation { y }^{ ' }\left( { y }^{ 2 }-x \right) =y is
  • { y }^{ 3 }-3xy=C
  • { y }^{ 3 }+3xy=C
  • { x }^{ 3 }-3xy=C
  • { y }^{ 3 }-xy=C
  • { x }^{ 3 }-xy=C
The solution of differential equation
4xy\cfrac { dy }{ dx } =\cfrac { 3{ \left( 1+x \right)  }^{ 2 }\left( 1+{ y }^{ 2 } \right)  }{ \left( 1+{ x }^{ 2 } \right)  } is 
  • \log { (1+y) } =\log { x } +2\tan { x } +constant
  • \log { \left( 1+{ y }^{ 2 } \right) } =3\log { \left( \cfrac { 1 }{ x } \right) } +6\tan ^{ -1 }{ x } +constant
  • 2\log { \left( 1+{ y }^{ 2 } \right) } =3\log { x } +6\tan ^{ -1 }{ x } +constant
  • None of the above
The solution of the differential equation \dfrac { dy }{ dx } +\sin { \left( \dfrac { y+x }{ 2 }  \right)  } +\sin { \left( \dfrac { y-x }{ 2 }  \right)  } =0 is
  • \log { \tan { \left( \dfrac { y }{ 2 } \right) } } =C-2\sin { x }
  • \log { \tan { \left( \dfrac { y }{ 4 } \right) } } =C-2\sin { \left( \dfrac { x }{ 2 } \right) }
  • \log { \tan { \left( \dfrac { y }{ 2 } +\dfrac { \pi }{ 4 } \right) } } =C-2\sin { x }
  • \log { \tan { \left( \dfrac { y }{ 2 } +\dfrac { \pi }{ 4 } \right) } } =C-2\sin { \left( \dfrac { x }{ 2 } \right) }
The solution of \dfrac {dy}{dx} + \sqrt{ \left( \dfrac {1-y^2}{1-x^2} \right) } = 0 is :
  • \tan^{-1} x + \cos^{-1} x = C
  • \sin^{-1} x + \sin^{-1} y = C
  • \sec^{-1} x + \text{cosec} ^{-1} x = C
  • None of the above.
An integrating factor of the differential equation \sin x \dfrac{dy}{dx} + 2 y \cos  x = 1 is
  • \sin^2 x
  • \dfrac{2}{\sin x}
  • \log |\sin x|
  • \dfrac{1}{\sin^2 x}
  • 2 \sin x
The general solution of the differential equation \left( x+y \right) dx+xdy=0 is
  • { x }^{ 2 }+{ y }^{ 2 }=C
  • 2{ x }^{ 2 }-{ y }^{ 2 }=C
  • { x }^{ 2 }+2xy=C
  • { y }^{ 2 }+2xy=C
The solution of the differential equation \left( { x }^{ 2 }-y{ x }^{ 2 } \right) \dfrac { dy }{ dx } +{ y }^{ 2 }+x{ y }^{ 2 }=0 is
  • \log { \left( \dfrac { x }{ y } \right) } =\dfrac { 1 }{ x } +\dfrac { 1 }{ y } +C
  • \log { \left( \dfrac { y }{ x } \right) } =\dfrac { 1 }{ x } +\dfrac { 1 }{ y } +C
  • \log { \left( xy \right) } =\dfrac { 1 }{ x } +\dfrac { 1 }{ y } +C
  • \log { \left( xy \right) } +\dfrac { 1 }{ x } +\dfrac { 1 }{ y } =C
The general solution of the differential equation xdy-ydx={y}^{2}dx is
  • y=\cfrac { x }{ C-x }
  • x=\cfrac { 2y }{ C+x }
  • (C+x)(2x)
  • y=\cfrac { 2x }{ C+x }
  • x=\cfrac { y }{ C-x }
The degree of the differential equation \left (\dfrac {d^{2}y}{dx^{2}}\right )^{3} + \left (\dfrac {dy}{dx}\right )^{2} + \sin\left (\dfrac {dy}{dx}\right )^{2} + \sin \left (\dfrac {dy}{dx}\right ) + 1 = 0 is
  • 3
  • 2
  • 1
  • None of the above
Solution of \cfrac { dx }{ dy } +mx=0, where m< 0 is:
  • x=C{ e }^{ my }
  • x=C{ e }^{ -my }
  • x=my+C
  • x=C
The solution of the differential equation \dfrac {dy}{dx} = e^{x - y} (e^{x} - e^{y}) is
  • e^{y} = (e^{x} + 1) + Ce^{-x}
  • e^{y} = (e^{x} - 1) + C
  • e^{y} = (e^{x} - 1) + Ce^{-x}
  • None of the above
The solution of \left( y-3{ x }^{ 2 } \right) dx+xdy=0 is
  • y(x)=\sin { x } +\cfrac { 1 }{ { x }^{ 2 } } +C
  • y(x)=\cos { x } -\cfrac { 1 }{ { x }^{ 2 } } +C\quad
  • y(x)={ x }^{ 2 }+\cfrac { C }{ x }
  • y(x)=\sqrt { x } +\cfrac { C }{ x }
Let f(x) be differentiable on the interval (0,\infty) and \lim _{ t\rightarrow x }{ \cfrac { { t }^{ 3 }f(x)+{ x }^{ 3 }f(t) }{ t-x }  } =2 gives a linear differential equation whose integrating factor is
  • { x }^{ 3 }
  • 1/{ x }^{ 3 }
  • { x }^{ 2 }
  • 1/{ x }^{ 2 }
The solution of x \log x \displaystyle\frac{dy}{dx}+y=1 is?
  • \log x=\displaystyle\frac{c}{(y-1)}
  • y\log x\displaystyle\frac{dy}{dx}+y=1
  • xy=\log (\log x)+c
  • \displaystyle\frac{x}{y}\log y=c
Solution of the differential equation (x^{2} + y^{3}) (2x^{2}dx + 3ydy) = 12x\ dx + 18y^{2}dy is
  • \dfrac {2}{3}x^{3} + \dfrac {3}{2}y^{2} = 6ln (x^{2} + y^{3}) + c
  • x^{2} + y^{3} = 9ln (x^{2} + y^{3}) + c
  • \dfrac {2}{3}x^{3} + \dfrac {3}{2}y^{2} = 6ln (x^{3} + y^{2}) + c
  • x^{3} + y^{2} = 6ln (x^{2} + y^{3}) + c
The solution of y' = e^{x - y} + x^{2} e^{-y} is
  • 3(e^{y} - e^{x}) - x^{3} = c
  • e^{y} - e^{x} - x^{3} = c
  • e^{y} - e^{x} + x^{3} = c
  • 3(e^{y} - e^{x}) + x^{3} = c
If y=\sqrt{(a-x)(x-b)}-(a-b)\tan^{-1}\sqrt{\displaystyle\frac{a-x}{x-b}}(a > b) then \displaystyle\frac{dy}{dx}=.
  • \sqrt{\displaystyle \frac{a-x}{x-b}}
  • \sqrt{(a-x)(x-b)}
  • 0
  • 1
The solution of the differential equation 3xy'-3y+{ \left( { x }^{ 2 }-{ y }^{ 2 } \right)  }^{ 1/2 }=0, satisfying the condition y(1)=1 is
  • 3\cos ^{ -1 }{ \left( \cfrac { y }{ x } \right) } =\ln { \left| x \right| }
  • 3\cos { \left( \cfrac { y }{ x } \right) } =\ln { \left| x \right| }
  • 3\cos ^{ -1 }{ \left( \cfrac { y }{ x } \right) } =2\ln { \left| x \right| }
  • 3\sin ^{ -1 }{ \left( \cfrac { y }{ x } \right) } =\ln { \left| x \right| }
The solution of equation \dfrac{dy}{dx}=\dfrac{ax+b}{cy+d} represents : 
  • A straight line if a=c=0 and b,d \neq 0
  • A parabola if a=2, c=0, d \neq 0
  • A huberbola if b=d=0, a and c\neq 0
  • A rectangular hyberbola of b=d=0, a=c=2
The solution of differential equation x \dfrac {dy}{dx} + y=y^2 is:
  • y=1+ cxy
  • y=\ln(cxy)
  • y+1=cxy
  • y=c+xy
The solution of the differential equation \left( x+3{ y }^{ 2 } \right) \dfrac { dy }{ dx } =y,\ y>0 is
  • \dfrac { x }{ y } =3y+c
  • x=2{ y }^{ 3 }+3{ y }^{ 2 }+c
  • y=3{ x }^{ 2 }+c
  • y=3x+c
The solution of the differential equation y'=\cfrac { 1 }{ { e }^{ -y }-x } , is
  • x={ e }^{ -y }\left( y+c \right)
  • y+{ e }^{ -y }=x+c
  • x={ e }^{ y }(y+c)
  • x+y={ e }^{ -y }+c
The general solution of the differential equation \cfrac { dy }{ dx } +\sin { \cfrac { x+y }{ 2 }  } =\sin { \cfrac { x-y }{ 2 }  } is
  • \log _{ e }{ \left| \tan { \cfrac { y }{ 2 } } \right| } =-2\cos { \cfrac { x }{ 2 } } +C
  • \log _{ e }{ \left| \tan { \cfrac { y }{ 2 } } \right| } =2\cos { \cfrac { x }{ 2 } } +C
  • \log _{ e }\left|{ \tan { \cfrac { y }{ 2 } } }\right| =2 \sin { \cfrac { x }{ 2 } } +C
  • \log _{ e }\left|{ \tan { \cfrac { y }{ 2 } } }\right| =-2\sin { \cfrac { x }{ 2 } } +C\quad
The differential equation \dfrac{dy}{dx} = e^x.e^y has solution ____________
  • e^x + e^y = C
  • e^{-x} + e^y = C
  • e^x + e^{-y} = C
  • e^{-x} + e^{-y} = C
The particular solution of differential equation \cfrac { dy }{ dx } =-4x{ y }^{ 2 },y(0)=1 is ______
  • y=\left( 2{ x }^{ 2 }+1 \right) =1
  • { x }^{ 2 }=\cfrac { 1 }{ { y }^{ 2 } }
  • y={ x }^{ 2 }+\log { x }
  • 4{ e }^{ x }+\cfrac { 1 }{ { y }^{ 2 } } =8\quad
The order of the differential equation whose general solution is y \, = \, c, \, cos \, 2x \, + \, c_2 \, cos^2x \, + \, c_3 \, sin^2x \, + \, c_4
  • 2
  • 4
  • 3
  • None of these
The solution of the differential equation 2x \dfrac{dy}{dx} = y; y(1) = 2 represents = ____.
  • parabola
  • ellipse
  • circle
  • line
What are the order and degree, respectively, of the differential equation
{ \left( \cfrac { { d }^{ 3 }y }{ d{ x }^{ 3 } }  \right)  }^{ 2 }={ y }^{ 4 }+{ \left( \cfrac { dy }{ dx }  \right)  }^{ 5 }\quad ?
  • 4,5
  • 2,3
  • 3,2
  • 5,4
What is the degree of the differential eqaution : \dfrac{d^3y}{dx^3}-6(\dfrac{dy}{dx})^2-4y=0
  • 1
  • 2
  • 3
  • None of these
the general solution of differential equation x^4 \, \frac{dy}{dx} \, + \, x^3 y \, + cosec \, xy \, =0,   is 
  • 2 cos ( x y ) + \dfrac{1}{x^2} = C
  • 2 cos ( x y ) + \dfrac{1}{y^2} = C
  • 2 sin y + \dfrac{1}{x^2} = C
  • 2 sin ( x y ) + \dfrac{1}{y^2} = C
Solution of the differential equation
\tan { y } .\sec ^{ 2 }{ x } dx+\tan { x } .\sec ^{ 2 }{ y } dy=0 is
  • \tan { x }+\tan { y }=k
  • \tan { x }-\tan { y }=k
  • \cfrac { \tan { x } }{ \tan { y } } =k
  • \tan { x }.\tan { y }=k
Let the function f satisfies f(x) .f'(-x) =f(-x) .f'(x) for all x and f(0) =3 
The value of f(x) .f(-x) for all x, is
  • 4
  • 9
  • 12
  • 6
The order of differential equation of family of all concentric circles centered at (h,k) is
  • 1
  • 2
  • 3
  • 4
The solution of \dfrac { dx }{ dy } -\dfrac { 2 }{ 3 } xy={ x }^{ 4 }{ y }^{ 3 } is
  • \dfrac { 1 }{ { x }^{ 3 } } =\dfrac { 3 }{ 2 } \left( 1-{ y }^{ 2 } \right) +c{ e }^{ -{ y }^{ 2 } }
  • \dfrac { 1 }{ { x }^{ 3 } } =\dfrac { 3 }{ 2 } \left( 1+{ y }^{ 2 } \right) +c{ e }^{ -{ y }^{ 2 } }
  • \dfrac { 1 }{ { x }^{ 4 } } =\dfrac { 3 }{ 2 } \left( 1-{ y }^{ 2 } \right) +c{ e }^{ { y }^{ 2 } }
  • \dfrac { 1 }{ { x }^{ 4 } } =\dfrac { 3 }{ 2 } \left( 1+{ y }^{ 2 } \right) +c{ e }^{ { y }^{ 2 } }
The solution of the equation \dfrac{dy }{dx} = e^{2x} is
  • \dfrac{e^{-2x}}{4} = y
  • y = \dfrac{e^{2x}}{2} + c
  • \dfrac{1}{4} e^{-2x} + cx^2 + d = y
  • \dfrac{1}{4} e^{-2x} + cx + d = y
The solution of x\dfrac{dy}{dx}+y\log{y}=xy{e}^{x} is
  • x\log{y}=(x+1){e}^{x}+c
  • \log{y}=(x-1){e}^{x}+c
  • (x-1)\log{y}=x{e}^{x}+c
  • x\log{y}=(x-1){e}^{x}+c
The solution of \sec ^{2}y\dfrac {dy}{dx}+2x\tan y=x^{3} is
  • \tan { y } =\frac { { x }^{ 2 } }{ 2 } +\frac { 1 }{ 2 } +c{ e }^{ -x^{ 2 } }
  • \tan { y } =\frac { { x }^{ 2 } }{ 2 } -\frac { 1 }{ 2 } +c{ e }^{ -x^{ 2 } }
  • \tan{ y} =\dfrac {x^{2}}{2}-\dfrac {1}{2}+c ({e}^{x})^{2}
  • \tan y=\dfrac {x^{2}}{2}+\dfrac{1}{2}+c({e^{x}})^{2}
The solution of \dfrac{dx}{dy} + \dfrac{x}{y} = x^2  is 
  • \dfrac{1}{y} = cx - xlogx
  • \dfrac{1}{x} = cy - ylogy
  • \dfrac{1}{x} = cx + xlogy
  • \dfrac{1}{y} = cx - ylogx
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