The solution of dxdy + xy = x2

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 Multiple Choice QuestionsMultiple Choice Questions

351.

The solution of 1 + x2dydx + 2xy - 4x2 = 0 is :

  • 3x1 + y2 = 4y3 + c

  • 3y(1 + x2) = 4x3 + c

  • 3x(1 + y2) = 4y3 + c

  • 3y(1 + y2) = 4x3 + c


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352.

The solution of dxdy + xy = x2 is :

  • 1y = cx - xlogx

  • 1x = cy - ylogy

  • 1x = cx + xlogy

  • 1y = cx - ylogx


B.

1x = cy - ylogy

dxdy + xy = x2 1x2dxdy + 1xy = 1Put 1x = t  - 1x2dxdy = dtdy - dtdy + ty = 1  dtdy - ty = - 1On compairing with dydx + Py = Q, we getP = - 1y, Q = - 1I.F. = epdx = e- 1ydy = 1yThe solution ist(I.F.) = QI.F.dy + c  t . 1y = - 1 .  1ydy +c  1x1y = - logy + c       1x = cy - y logy


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353.

The differential equation obtained by eliminating the arbitrary constants a and b from xy = aex + be- x is

  • xd2ydx2 +2dydx - xy = 0

  • xd2ydx2 +2ydydx - xy = 0

  • xd2ydx2 +2dydx + xy = 0

  • d2ydx2 +dydx - xy = 0


354.

The solution of x + y +1dydx = 1 is

  • y = (x + 2) + cex

  • y = - (x + 2) + cex

  • x = - (y + 2) + cey

  • x = (y + 2)2 + cey


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355.

The solution of dydx = y2xy - x2 is

  • eyx = kx

  • eyx = ky

  • exy = kx

  • e - yx = ky


356.

The solution of dydx +1 = ex +y is

  • e - x + y +x + c = 0

  • e - x + y -x + c = 0

  • e x + y +x + c = 0

  • e x + y -x + c = 0


357.

The solution of the differential equation

dydx = xy + yxy + x is

  • x + y = logcyx

  • x + y = logcxy

  • x - y - logcxy

  •  y - x = logcxy


358.

The solution of the differential equation

dydx = x - 2y + 12x - 4y is

  • (x - 2y)2 + 2x = c

  • (x - 2y)2 + x = c

  • (x - 2y)2 + 2x2 = c

  • (x - 2y) + x2 = c


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359.

The solution of the differential equation dydx - ytanx = exsecx is

  • y = excosx + c

  • ycosx = ex + c

  • y = exsinx + c 

  • ysinx = ex + c


360.

The solution of the differential equation

xy2dy - x3 + y3dx = 0 is

  • y3 = 3x3 + c

  • y3 = 3x3 logcx

  • y3 = 3x3 + logcx

  • y3 +3x3 = logcx


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