If xy = A sin(x) + B cos(x) is the solution of  the differen

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 Multiple Choice QuestionsMultiple Choice Questions

121.

The general solution of the differential equation dydx = eyex + e- x + 2x is

  • e- y = ex + e- x + x2 + C

  • e- y = e- x - ex - x2 + C

  • e- y = - e- x - ex - x2 + C

  • ey = e- x + ex + x2 + C


122.

The order and degree of the differential equation d2ydx313 = 2d2ydx2 + cos2x3 are, respectively

  • 3 and 1

  • 3 and 3

  • 1 and 3

  • 3 and 2


123.

The differential equation representing the family of curves given by y = ae3x + b, where a and b are arbitrary constants, is

  • d2ydx2 + 3dydx - 2y = 0

  • d2ydx2 - 3dydx = 0

  • d2ydx2 - 3dydx - 2y = 0

  • d2ydx2 + 3dydx = 0


124.

An integrating factor of the differential equation xdy - ydx + x2exdx = 0 is

  • 1x

  • log1 + x2

  • 1 + x2

  • x


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125.

The solution of the differential equation xdydx = y1 + logx is

  • y = log(x) + C

  • y = C1 + logx

  • y = Cx + logx

  • y = C1 + logx


126.

The solution of the differential equation logxdydx + yx = sin2x is

  • ylogx = C - 12cosx

  • ylogx = C + 12cos2x

  • ylogx = C - 12cos2x

  • xylogx = C - 12cos2x


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127.

If xy = A sin(x) + B cos(x) is the solution of  the differential equation xd2ydx2 - 5adydx + xy = 0, then the value of a is

  • 25

  • 52

  • - 25

  • - 52


C.

- 25

Given,

xy = A sin(x) + B cos(x)        ...(i)

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

xdydx + y = Acosx - Bsinx  ...iiand xd2ydx2 + dydx + dydx = - Asinx - Bcosxand xd2ydx2 + 2dydx = - xy     from Eq. (i) xd2ydx2 + 2dydx + xy = 0On Comparing with  xd2ydx2 - 5adydx + xy = 0we get- 5a = 2  a = - 25


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128.

The solution of the differential equation dydx = 3e2x + 3e4xex + e- x is

  • y = e3x + C

  • y = 2e2x + C

  • y = ex + C

  • y = e4x + C


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129.

The order and degree of the differential equation of the family of circles of fixed  radius r with centres on the y-axis, are respectively

  • 2, 2

  • 2, 3

  • 1, 1

  • 1, 2


130.

The solution of the differential equation (kx - y2 ) dy = (x2 - ky) dx is

  • x3 - y3 = 3kxy + C

  • x3 + y3 = 3kxy + C

  • x2 - y2 = 2kxy + C

  • x2 + y2 = 2kxy + C


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