The differential equation of the family of curve y = Ae3x + Be5x,

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 Multiple Choice QuestionsMultiple Choice Questions

301.

Solve dydx = y2xy - x2

  • y = cex/y

  • y = ce-y/x + x

  • y = cey/x

  • xy = cey/x


302.

Solve xcosxdydx + yxsinx + cosx = 1

  • y = xtanx + sinx +c

  • x = ytanx + c

  • yxsecx = tanx + c

  • xycosx = x +c


303.

Differential equation of the family of curve y = a cos(µx) + b sin(µx), where a, b are arbitrary constants, is given by

  • d2ydx2 + μy = 0

  • d2ydx2 + μ2y = 0

  • d2ydx2 - μ2y = 0

  • None of these


304.

The differential equation of all circles which pass through the origin and whose centres lie on y-axis is

  • x2 - y2dydx - 2xy = 0

  • x2 - y2dydx + 2xy = 0

  • x2 - y2dydx - xy = 0

  • x2 - y2dydx + xy = 0


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305.

The differential equation of the family of curve y = Ae3x + Be5x, where A, B are arbitrary constants, is

  • d2ydx2 + 8dydx + 15 = 0

  • d2ydx2 - 8dydx + 15 = 0

  • d2ydx2 - dydx + y = 0

  • None of these


B.

d2ydx2 - 8dydx + 15 = 0

Let      y = Ae3x + Be5x   dydx = 3Ae3x + 5Be5x d2ydx2 = 9Ae3x + 25Be5xd2ydx2 + 15y = 9Ae3x + 25Be5x + 15Ae3x + 15Be5x                    = 24Ae3x + 40Be5x                    = 83Ae3x + 5Be5x = 8dydx d2ydx2 - 8dydx + 15 = 0


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306.

Solution of the differential equation xdydx = y + x2 + y2 is

  • y - x2 + y2 = cx2

  • y + x2 + y2 = cx2

  • x + x2 + y2 = cy2

  • x - x2 + y2 = cy2


307.

The differential equation whose solution represents the family y = ae3x + bex is given by

  • d2ydx2 - 4dydx - 3y = 0

  • d2ydx2 + 4dydx - 3y = 0

  • d2ydx2 - 4dydx + 3y = 0

  • None of the above


308.

Solve 2dydx = yx + yx2

  • y = x + Cxy

  • y = x - Cxy

  • y = x + Cyx

  • y = x + Cy


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309.

Solve x +2y3dydx = y, y >0

  • y = x3 + Cy

  • x = y3 + Cy

  • y = x3 - Cy

  • x = y3 - Cy


310.

The solution of the differential equation xdydx = y + xtanyx is

  • sinxy = x + C

  • sinyx = Cx

  • sinxy = Cy

  • sinyx = Cy


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