The solution of differential equation x2 + y2 

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 Multiple Choice QuestionsMultiple Choice Questions

211.

The solution of the differential equation x +2y3dydx = Y is

  • y3 + Cx = y

  • xy42 + xy = Cy

  • y3 + Cy = x

  • x + 2y3 = y + C


212.

The solution ofthe differential equation

dydx = ylogy - logx + 1x is

  • x = yecy

  • y = xecy

  • x = yecx

  • None of these


213.

The solution of the differential equationdydx + siny + x2 + siny - x2 = 0 is

  • logtany2 = C - 2sinx

  • logtany4 = C - 2sinx2

  • logtany2 + π4 = C - 2sinx

  • logtany2 + π4 = C - 2sinx2


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214.

The solution of differential equation x2 + y2 - 2xydydx = 0 is

  • x2 + y2 = xC

  • x2 - y2 = xC

  • x2 + y2 = C

  • x2 - y2 = C


B.

x2 - y2 = xC

Given differential equation isx2 + y2 - 2xydydx = 0which is homogeneous        degree of each term is same i.e., 2It can be rewritten as   dydx = x2 + y22xy = 12xy + yxPut y = vx  dydx = v + xdvdx, so thatthe differential equation becomesv +xdvdx = 121v + v  xdvdx = 1 + v22v - v xdvdx = 1 - v22v

    2v1 - v2dv = 1xdx - log1 - v2 = logx - logC        x1 - v2 = C          x2 - y2x = C        v = yx

Hence, x2 - y2 = xC is the required solution.


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215.

The solution of differential equation dydx = x2logx + 1siny + ycosy is

  • ysiny = x2logx + C

  • y = x2 + logx + C

  • ysiny = x2 + C

  • None of these


216.

Solution of 2ysinxdydx = 2sinxcosx - y2cosx, x = π2, y = 1 is given by

  • y2 = sin(x)

  • y = sin2(x)

  • y2 = cos(x) + 1

  • None of these


217.

Solution of x2dydx - xy = 1 +cosyx is

  • tany2x = C - 12x2

  • tanyx = C + 1x

  • cosyx = 1 + Cx

  • x2 = C + x2tanyx


218.

The solution of dydx = cosx2 - ycscx where y = 2, when x = π2 is

  • y = sinx + cscx

  • y = tanx2 + cotx2

  • y = 12secx2 + 2cosx2

  • None of the above


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219.

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

  • tanx + y + secx + y = x + C

  • tanx + y - secx + y = x + C

  • tanx + y - secx + y + x + C = 0

  • None of the above


220.

The solution of differential equation

4xydydx = 31 +x21 + y21 +x2 is

  • log1 + y = logx + 2tanx + C

  • log1 + y2 = 3log1x + 6tan-1x + C

  • log1 + y2 = 3logx + 6tan-1x + C

  • None of the above


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