The integrating factor of the differential equation x .

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 Multiple Choice QuestionsMultiple Choice Questions

271.

General solution of differential equations dydx + y = 1y  1 is

  • log11 - y = x + C

  • log1 - y = x + C

  • log1 + y = x + C

  • log11 - y = - x + C


272.

The degree of the differential equation 1 + dydx22 = d2ydx2 is

  • 3

  • 2

  • 1

  • 4


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273.

The integrating factor of the differential equation x . dydx + 2y = x2 is x  0

  • x

  • logx

  • x2

  • elogx


C.

x2

We have, x . dydx + 2y = x2              dydx + 2xy = xThe above dlfferential equation is a linear differential equation Integrating factor = e2xdx                                 = e2logx                                 = elogx2                                 = x2


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274.

The order of the differential equation

ydydx = xdydx + dydx3 is

  • 1

  • 2

  • 3

  • 4


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275.

The general solution of the differential equation (x + y)dx + xdy = 0 is

  • x2 + y2 = c

  • 2x2 - y2

  • x2 + 2xy = c

  • y2 + 2xy = c


276.

The order and degree of the differential 1 + 3dydx23 = 4d3ydx3 are

  • 1, 2/3

  • 3, 1

  • 3, 3

  • 1, 2


277.

The differential equation of all straight lines passing through the point (1, - 1)is

  • y = x + 1dydx + 1

  • y = x + 1dydx - 1

  • y = x - 1dydx + 1

  • y = x - 1dydx - 1


278.

The solution of the differential equation d2ydx2 = e- 2x is

  • y = e- 2x4

  • y = e- 2x4 + cx + d

  • y = e- 2x4 + cx2 + d

  • y = e- 2x4 + c + d


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279.

The solution of the differential equation dydx + sin2y = 0 is

  • x = coty + c

  • y = cotx + c

  • x = 2cscycoty + c

  • y = 2sinycosy + c


280.

Family y = Ax + A3 ofcurve is represented by the differential equation ofdegree

  • 3

  • 2

  • 1

  • None of these


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