The differential coefficient of log10(x) with respect to logx(10)

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261.

The general solution of the differential equation 1 - x2y2 . dx = y . dx + x . dy is

  • sinxy = x +C

  • sin-1xy + x = C

  • sinx +C = xy

  • sinxy + x = C


262.

If m and n are order and degree of the differential equation y''5 + y''3y''' + y''' = sinx, then

  • m = 3, n = 5

  • m = 3, n = 1

  • m = 3, n = 3

  • m = 3, n = 2


263.

The order and degree of the differential equation y = xdydx + 2dydx is

  • 1, 2

  • 1, 3

  • 2, 1

  • 1, 1


264.

The general solution of the differential equation dydx + yx = 3x is

  • y = x - Cx

  • y = x + Cx

  • y = x2 - Cx

  • y = x2 + Cx


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265.

The order of differential equation of all circles of given radius 'a' is

  • 1

  • 4

  • 3

  • 2


266.

The solution of differential equation xdydx + 2y = x2 is

  • y = x4 + Cx2

  • y = x2 + C4x2

  • y = x4 + C4x2

  • y = x24 + C


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267.

The differential coefficient of log10(x) with respect to logx(10) is

  • 1

  • - log10x2

  • logx102

  • x2100


B.

- log10x2

Let u = log10x and v = logx10 u = logexloge10 and v = loge10logexNow dudx = 1xloge10and dvdx = loge10- 1xlogex2  dudv = dudxdvdx = 1xloge10 ÷ loge10xlogex2           = - logex2loge102 = - logexloge102           = - log10x2


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268.

The solution for the differential equation dydx + dxx = 0 is

  • 1y + 1x = C

  • logxlogy = C

  • xy = C

  • x + y = C


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269.

The order and degree of the differential equation 1 + dydx2 + sindydx34 = d2ydx2

  • order = 2, degree = 3

  • order = 2, degree = 4

  • oreder = 2, degree = 34

  • order = 2, degree = not defined


270.

Integrating factor of xdydx - y = x4 - 3x is

  • x

  • log(x)

  • 1x

  • - x


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