The solution of the differential equation dydx = 2

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 Multiple Choice QuestionsMultiple Choice Questions

201.

The degree and order of the differential equation 1 + dydx373 = 7d2ydx2 respectively are

  • 3 and 7

  • 3 and 2

  • 7 and 3

  • 2 and 3


202.

The particular solution of the differential equation

y1 + logxdxdy - xlogx = 0, when, x = e, y = e2 is

  • y = exlog(x)

  • ey = xlog(x)

  • xy = elog(x)

  • ylog(x) = ex


203.

If sinx  is the integrating factor (IF) of the linear differential equation dydx + Py = Q, then P is

  • logsinx

  • cosx

  • tanx

  • cotx


204.

The solution of the differential equation

dydx = tanyx + yx is

  • cosyx = cx

  • sinyx = cx

  • cosyx = cy

  • sinyx = cy


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205.

The differential equation of all parabolas whose axis is Y-axis, is

  • xd2ydx2 - dydx = 0

  • xd2ydx2 + dydx = 0

  • d2ydx2 - y = 0

  • d2ydx2 - dydx = 0


206.

The particular solution of the differential equation xdy + 2ydx = 0, when x = 2, y = 1 is

  • xy = 4

  • x2y = 4

  • xy2 = 4

  • x2y2 = 4


207.

The general solution of the equation dydx = y2 - x2yx + 1 is

  • y2 = (1 + x)log(1 + x) - c

  • y2 = 1 + xlogc1 - x - 1

  • y2 = 1 - xlogc1 - x - 1

  • y2 = 1 + xlogc1 + x - 1


208.

The general solution of the differential equation dydx + sinx + y2 = sinx - y2 is

  • logetany2 = - 2sinx2 +C

  • logetany4 = 2sinx2 +C

  • logetany2 = - 2sinx2 +C

  • logetany4 = - 2sinx2 +C


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209.

The function y specified implicitly by the relation 0yetdt + 0xcostdt = 0 satisfies the differential equation

  • e2yd2ydx2 + dydx2 = sinx

  • eyd2ydx2 + dydx2 = sin2x

  • ey2d2ydx2 + dydx2 = sinx

  • eyd2ydx2 + dydx2 = sinx


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210.

The solution of the differential equation dydx = 2ex - y + x2e- y is

  • ey = 2ex + x33 + C

  • e- y = 2ex + x- 33 + C

  • e- y = 2ex + x33 + C

  • ey = 2e- x + x33 + C


A.

ey = 2ex + x33 + C

Given, dydx = 2ex - y + x2e- y      dydx = 2ex . 1ey + x2 . 1ey      dydx = 1ey2ex + x2    eydy = 2ex + x2dxOn Integrating both sides, we get     eydy = 2ex + x2dx            ey = 2ex + x33 + C


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