The differential equation of all parabolas whose axes are paralle

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 Multiple Choice QuestionsMultiple Choice Questions

51.

Solution of the differential equation xdy - ydx = 0 represents a

  • parabola

  • circle

  • hyperbola

  • straight line


52.

The general solution of the differential equation

dydx = ey + x + ey - x is

  • e- y = ex - e- x + c

  • e- y = e- x - ex + c

  • e- y = ex + ex + c

  • ey = ex + e- x + c


53.

The order of the differential equation

d2ydx2 = 1 + dydx2 is

  • 3

  • 2

  • 1

  • 4


54.

The degree of the differential equation

1 + dydx253 = d2ydx2 is

  • 1

  • 5

  • 103

  • 3


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55.

The differential equation of all parabolas whose axes are parallel to y-axis, is

  • d3ydx3 = 0

  • d2ydx2 = 0

  • d2ydx2 + dydx = 0

  • d2ydx2 + dydx + y = 0


A.

d3ydx3 = 0

The equation of a member of the family of parabolas having axis parallel to y-axis is y = Ax + Bx + C, where A, B and C are arbitrary constants.

  dydx = 2Ax + B d2ydx2 = 2A d3ydx3 = 0


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56.

The solution of the differential equation dydx = ey + x + ey - x is

  • e- y = ex - e- x + c, c integrating constant

  • e- y = e- x - ex + c, c integrating constant

  • e- y = ex + e- x + c, c integrating constant

  • e- y + ex - e- x = c, c integrating constant


57.

If x = etsint, y = etcost, then d2ydx2 at x = π is

  • 2eπ

  • 12eπ

  • 12eπ

  • 2eπ


58.

The value of dydx at x = π2, where y is given by y = xsinx + x, is

  • 1 + 12π

  • 1

  • 12π

  • 1 - 12π


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59.

The order and degree of the following differential equation 1 + dydx252 = d3ydx3 are respectively

  • 3, 2

  • 3, 10

  • 2, 3

  • 3, 5


60.

The differential equation of the family of circles passing through the fixed points (a, 0) and (- a, 0) is

  • y1(y2 - x2) + 2xy + a2 = 0

  • y1y2 + xy + a2x2 = 0

  • y1(y2 - x2 + a2) + 2xy = 0

  • y1(y2 + x2) - 2xy + a2 =  0


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