The solution of the differential equation dydx + 2

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 Multiple Choice QuestionsMultiple Choice Questions

231.

The solution of the differential equation dydx = y tanx - 2 sinx, is

  • y sinx = c + sin2x

  • y cosx = c + 12sin2x

  • y cosx = c - sin2x

  • y cosx = c + 12cos2x


232.

The differential equation of system of concentric circles with centre (1, 2) is :

  • x - 2 + y - 1dydx = 0

  • x - 1 + y - 2dydx = 0

  • x + 1dydx + y - 2 = 0

  • x + 2dydx + y - 1 = 0


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233.

The solution of the differential equation dydx + 2yx1 +x2 = 11 +x22 is :

  • y(1 + x2) = c + tan-1(x)

  • ylog1 + x2 = c + tan-1x

  • y1 + x2 = c + tan-1x

  • y1 + x2 = c + sin-1x


A.

y(1 + x2) = c + tan-1(x)

dydx + 2yx1 +x2 = 11 +x22On comparing the given differential equation with linear differential equation        dydx + py = QWe get P = 2x1 + x2 and Q = 11 + x22Now,  IF = ePdx = e2x/1 +x2dx              = elog1 + x2 = 1 + x2 y1 + x2 = 11 + x221 + x2dx + c y1 + x2 = 11 + x2dx + c y1 + x2 = c + tan-1x


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234.

The solution of the differential equation xdy - ydx = x2 + y2dx is :

  • x+  x2 + y2 = cx2

  • y-  x2 + y2 = cx

  • x -  x2 + y2 = cx

  • y+  x2 + y2 = cx2


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235.

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

  • y = ex - y + x2e- y + c

  • ey - ex = 13x3 + c

  • ey + ex = 13x3 + c

  • ex - ey = 13x3 + c


236.

The integrating factor of the differential equation dydx + 1xy = 3x is :

  • x

  • in x

  • 0


237.

The solution of the differential equation sec2(x)tan(y))dx + sec2(y)tan(x))dy = 0 is :

  • tanytanx = c

  • tanytanx = c

  • tan2x tany= c

  • None of these


238.

The differential equation of all straight lines passing through origin is :

  • y = xdydx

  • dydx = y + x

  • dydx = y - x

  • None of these


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239.

To reduce the differential equation dydx = Py = Qx . yn to the linear form, the substitution is :

  • v = 1yn

  • v = 1yn - 1

  • v = yn

  • v = yn - 1


240.

Integrating factor of the differential equation dydx +Pxy = Qx is :

  • P dx

  • Q dx

  • eP dx

  • eQ dx


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