The solution of differential equation (ylog(x) - 1)ydx = xdy is

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 Multiple Choice QuestionsMultiple Choice Questions

321.

The solution of the equation dydx = 1x + y + 1 is

  • x + y = Cey - 2

  • x + y = Clog(y) - 4

  • log(x+ y + 2) = Cy

  • log(x + y + 2) = C + y


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322.

The solution of differential equation (ylog(x) - 1)ydx = xdy is

  • ylogex + Cx = 1

  • logxe + Cxx = y

  • logCx2 + ex2y = x

  • None of these


D.

None of these

Given differential equation is   ylogx - 1ydx = xdy                    dydx = ylogx - 1yx                              = y2logxx - yx           dydx + yx = y2logxx 1y2dydx + y-1x = logxx       ...iPut y-1 = v - y-2dydx = dvdx     y-2dydx = - dvdxFrom Eq. (ii), we have - dvdx + vx = logxx dvdx - vx = logxx             ...iiTlus is linear differential equationHere, IF = e- 1xdx = e- logx = 1xSo, soluton is v . IF = IF . Q dx +C

v . 1x = 1x- logxxdx + C v . 1x = - logxx2dx +C               = - logx- 1x + 1x . 1xdx + C 1x . y = logxx + 1x +C     v = 1y       1 = ylogx +1 +Cx       1 = ylogx + loge + Cx                        1 = loge      1 = yloge . x + Cx


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323.

The solution of the differential equation a + xdydx + xy = 0 is

  • y = Ce232a  - xx + a

  • y = Ce23a  - xx + a

  • y = Ce232a  + xx + a

  • y = Ce- 232a  - xx + a


324.

The general solution of the differential equation dydx = ytanx - y2secx is

  • tanx = C + secxy

  • secy = C + tanyx

  • secx = C + tanxy

  • tany = C + secxx


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325.

The degree of the differential equation satisfying 1 - x2 + 1 - y2 = ax - y is

  • 1

  • 2

  • 3

  • None of the above


326.

The solution of the differential equation y - xdydx = ay2 + dydx is

  • y = C(x + a)(1 - ay)

  • y = C(x + a)(a + ay)

  • y = C(x - a)(1 - ay)

  • None of the above


327.

The solution of differential equation (2y - 1)dx - (2x + 3)dy = 0 will be

  • 2x - 12y + 3 = C

  • 2y + 12x - 3 = C

  • 2x + 32y - 1 = C

  • 2x - 12y - 1 = C


328.

The solution of the differential equation dydx = xlogx2 + xsiny + ycosy will be

  • ysin(y) = x2log(x) + C

  • ysin(y) = x2 + C

  • ysin(y) = x2 + lo(x) + C

  • ysin(y) = xlog(x) + C


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329.

The order and degree of the differential equation y'4 = 1 - y''' are respectively.

  • 3, 4

  • 1, 2

  • 3, 2

  • 3, 1


330.

The differential equation of the family of circles having centre on Y-axis and radius 4 is

  • x2 - 4dydx2 + x2 = 0

  • x2 - 9dydx2 + x2 = 0

  • x2 - 9dydx + x2 = 0

  • x2 - 16dydx2 + x2 = 0


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