The differential equation for the family of curve x2 + y2 - 2ay =

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 Multiple Choice QuestionsMultiple Choice Questions

281.

The degree and order of the differential equation of the family of all parabolas whose axis is X-axis, are respectively

  • 2, 1

  • 1, 2

  • 3, 2

  • 2, 3


282.

Solution of the differential equation ydx - xdy = x2ydx

  • yex2 = cx2

  • ye- x2 = cx2

  • y2ex2 = cx2

  • y2e- x2 = cx2


283.

The solution of the differential equation 1 + y2 + x - etan-1ydydx = 0 is

  • x - 2 = e2tan-1y + c

  • 2xetan-1y = e2tan-1y + c

  • xetan-1y = tan-1y + c

  • xe2tan-1y = etan-1y + c


284.

Solution of the differential equation (x + y - 1)dx + (2x+ 2y - 3)dy = 0

  • y + x + log (x + y - 2) = c

  • y + 2x + log (x + y - 2) = c

  • 2y + x + log (x + y - 2) = c

  • 2y + 2x + log (x + y - 2) = c


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285.

The differential equation for the family of curve x2 + y2 - 2ay = 0, where a is an arbitrary constant, is

  • 2(x2 - y2)y' = xy

  • 2(x2 + y2)y' = xy

  • (x2 - y2)y' = 2xy

  • (x2 + y2)y' = 2xy


C.

(x2 - y2)y' = 2xy

The given equation is

x2 + y2 - 2ay = 0         ...(i)

On differentiating w.r.t. .x, we get

2x + 2yy' = 2ay      dydx = y'         a = x + yy'y'On putting the value of a in Eq. (i), we get           x2 + y2 - 2x + yy'y'y = 0   x2 + y2y' - 2yx + yy' = 0 x2y' + y2y' - 2xy - 2y2y' = 0                         x2 + y2y' = 2xy


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286.

Solution of the differential equation cosxdydx + ysinx = 1 is

  • ysecx + tanx = c

  • ysecx = tanx + c

  • ytanx = secx + c

  • ytanx = secxtanx + c


287.

The solution of the differential equation ydx + (x + x2y)dy = 0 is

  • - 1xy = c

  • - 1xy + logy = c

  • 1xy = logy + c

  • logy = cx


288.

The differential equation of the equation y2 = m(x2 - a2) is

  • ydydx = yd2ydx2 + dydx2x

  • ydydx = yd2ydx2 - dydx2x

  • yd2ydx2 = yd2ydx2 + dydx2x

  • None of the above


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289.

dydx = ax +hby + k will be parabola, if

  • a = 0

  • b = 1

  • a = 1

  • None of these


290.

The number of real solutions of tan-1xx + 1 + sin-1x2 + x + 1 = π2 is

  • zero

  • one

  • two

  • infinite


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