The solution of the differential equationdydx = 1 

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 Multiple Choice QuestionsMultiple Choice Questions

221.

The order and power of differential equation

d2ydx2 + 7dydx + ydx = sinx is

  • 1, 3

  • 3, 1

  • 1, 2

  • 2, 1


222.

The solution of differential equation xcos2ydx = ycos2xdx is

  • xtanx - ytany - logsecx/secy = c

  • ytanx - xtanx - logsecx.secy = c

  • xtanx - ytany + logsecx.secy = c

  • None of the above


223.

Differential equation of those circles which passes through origin and their centres lie on y-axis will be

  • x2 - y2dydx +2xy = 0

  • x2 - y2dydx =2xy

  • x2 - y2dydx =xy

  • x2 - y2dydx +xy = 0


224.

The differential equation of all circles touching the axis of y at origin and centre on the x-axis is given by

  • xydydx - x2 + y2 = 0

  • 2xydydx - x2 - y2 = 0

  • x2 + y2dydx - 2xy = 0

  • None of these


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225.

The solution of the differential equation

e- 2x - yxdxdy = 1 is given by

  • e2x = 2x + c

  • ye- 2x = x + c

  • y = x

  • None of these


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226.

The solution of the differential equation

dydx = 1 - y21 - x2 is

  • sin-1y - sin-1x = c

  • sin-1y + sin-1x = c

  • sin-1xy = 2

  • None of these


A.

sin-1y - sin-1x = c

Given, dydx = 1 - y21 - x2dy1 - y2 = dx1 - x2On integrating both sides, we getsin-1y - sin-1x = c


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227.

The solution of differential equation (1 + x)ydx + (1 - y)x dy = 0 is

  • logexy + x - y = c

  • logexy + x + y = c

  • logexy - x + y = c

  • logexy - x + y = c


228.

The differential equation of all circles which passes through the origin and whose centre lies on y-axis is

  • x2 - y2dydx - 2xy = 0

  • x2 - y2dydx + 2xy = 0

  • x2 - y2dydx - xy = 0

  • x2 - y2dydx + xy = 0


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229.

The general solution of y2dx + (x2 - xy + y2)dy = 0 is

  • tan-1xy + logy + c = 0

  • 2tan-1xy + logx + c = 0

  • logy + x2 + y2 + logy + c = 0

  • sinh-1xy + logy + c = 0


230.

The solution of the equation d2ydx2 = e- 2x is

  • y = 14e- 2x + cx2 +d

  • y = 14e- 2x + cx +d

  • y = 14e- 2x + cx2 +d

  • y = 14e- 2x + cx3 +d


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