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CBSE Questions for Class 12 Commerce Maths Differential Equations Quiz 11 - MCQExams.com

The solution of x2dyy2dx+xy2(xy)dy=0, is?
  • log|xyxy|=y22+C
  • log|xyxy|=x22+C
  • log|xyxy|=x22+C
  • log|xyxy|=x+C
Solution of equation dydx=ydd(ϕ(x))y2ϕ(x) is
  • y=ϕ(x)+cx
  • y=ϕ(x)x+c
  • y=ϕ(x)x+c
  • y=ϕ(x)+x+c
An equation containing an independent variable, dependent variable, and differential coefficients of the dependent variable with respect to the independent variable is called a/an _______
  • Differential equation
  • Continuous function
  • Discontinuous function
  • Integral equation
The integrating factor of the equation sinydydx=cosy(1xcosy) is 
  • ex
  • ex
  • esecy
  • None of these
Solution of differential equation dydx+xsin2y=sinycosy is-
  • tany=(x1)+Cex
  • coty=(x1)+Cex
  • tany=(x1)ex+c
  • coty=(x1)ex+c
Consider the differential equation y2dx+(x1y)dy=0
If y(1)=1, then x is given by:
  • 42ye1ye
  • 31y+e1ye
  • 1+1ye1ye
  • 11y+e1ye
Solution of differential equation dydx+xsin2y=sinycosy is-
  • tany=(x1)+cex
  • coty=(x1)+cex
  • tany=(x1)ex+C
  • coty=(x1)ex+C


    (where C is an arbitrary constant)
Solve the differential equation:
(ey+1)cosx dx+eysinx dy=0
  • sinx(ey+1)=c
  • sinx(ey+1)=c
  • sinx(e2y+1)=c
  • cosx(ey+1)=c
Let the population of rabbits surviving at a time t be governed by the differential equation dp(t)dt=12p(t)200. If p(0)=100 , then p(t) equals:
  • 600500et/2
  • 400300et/2
  • 400300et/2
  • 300200et/2
The solution of y5x+yxdydx=0 is
  • x44+15(xy)5=C
  • x54+15(xy)4=C
  • (xy)5+x44=C
  • (xy)4+x55=C
Suppose y=y(x) satisfies the differential equation ydx+y2dy=xdy. If y(x)>0xϵR and y(1)=1, then y(-3) equals
  • 1
  • 2
  • 3
  • 5
y=(c1+c2x+x2)ex is a solution of
  • d2ydx2+y=0
  • d2ydx2+xy=0
  • d2ydx2=x
  • d2ydx22dydx+y=2ex
An integrating factor of the differential equation xdydxy=x3;x>0 is ________
  • 1x
  • -x
  • 1x
  • x
The solution of the differential equation dydxky=0,y(0)=1, approaches zero when x, if
  • k = 0
  • k > 0
  • k < 0
  • k may be any real value
Solution of the differential equation
x=1+(xydydx)+(x2y2)2!(dydx)3+......... is
  • y=in(x)+C
  • y=(inx)2+C
  • y=±(inx)2+C
  • xy=xy+K
Solution of differential equation 2xydydx=x2+3y2.
  • x3+y2=px2
  • x22+y3x=y2+p
  • x2+y3=px
  • x2+y2=px3
y=32x  Find  dydx
  • 32x
  • 22x
  • 23x
  • 24x
Let y=y(x) be a solution of the differential equation, 1x2dydx+1y2=0,|x|<1.
If y(12)=32, then y(12) is equal to:
  • 32
  • 12
  • 32
  • 12
Equation of the curve in which the subnormal is twice the square of the ordinate is given by 
  • logy=2x+logc
  • y=ce2x
  • logy=2xlogc
  • None of these
The solution of dydx+x1x2y=xy, is given by
  • 3y+(1x2)=C(1x2)1/4
  • 32y+1(1x2)=C(1x2)3/2
  • 3y(1x2)=C(1x2)3/2
  • None of these
State true or false.
dydx+y=5 is a differential equation of the type dydx+PY=Q but it can be solved using the variable separable method also.
  • True
  • False
The solution of dydx=(x+y)2(x+2)(y2) is given by
  • (x2)4(1+2yx)=ke2y/x
  • (x2)4(1+2(y2)(x+2))=ke2(y2)(x+2)
  • (x2)3(1+2(y2)x+2)=ke2(y2)(x+2)
  • none of these
If (y22x2y)dx+(2ky2x3)dy=0 then the value of xyy2x2 is 
  • y2+x
  • xy2
  • any constant
  • None of these
0:0:1


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