The solution of dydx + 1 = cscx +&t

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 Multiple Choice QuestionsMultiple Choice Questions

151.

Solution of the equation xdydx2 + 2xydydx + y = 0 is :

  • x + y = a

  • x - y = a

  • x2 + y2 = a2

  • x + y = a


152.

The solution of differential equation (x + y )(dx - dy) = dx + dy is :

  • x - y = kex - y

  • x + y = kex + y

  • x + y = k(x - y)

  • x + y = kex - y


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153.

The solution of dydx + 1 = cscx +y is  :

  • cosx +y +x = c

  • cosx +y = c

  • sinx +y + x = c

  • sinx +y + sinx +y = c


A.

cosx +y +x = c

  dydx + 1 = cscx +yLet     x + y = t 1 + dydx = dtdx    dtcsct = dxOn integrating both sides, we get

                sintdt = dx            - cost = x +c cosx + y + x = c


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154.

The order of the differential equation

d2ydx23 = 1 + dydx12 is :

  • 2

  • 3

  • 12

  • 4


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155.

The integrating factor of the differential equation cosxdydx + ysinx = 1 is :

  • cosx

  • tanx

  • sinx

  • secx


156.

Solution of the differential equation tan(y) . sec2(x)dx + tan(x) · sec2(y)dy = 0 is

  • tan(x) + tan(y) = k

  • tan(x) - tan(y) = k

  • tanxtany = k

  • tanx . tany = k


157.

The differential equation of all non-horizontal lines in a plane is :

  • d2ydx2 = 0

  • dxdy = 0

  • dydx = 0

  • d2xdy2 = 0


158.

The order and degree of the differential equation y + d2ydx2 = x + dydx32 are :

  • 2, 2

  • 2, 1

  • 1, 2

  • 2, 3


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159.

The solution of 2(y + 3) - xy dydx = 0 with y = - 2,when x = 1 is

  • (y + 3) = x2

  • x2(y + 3) = 1

  • x4(y + 3) = 1

  • x2(y + 3)3 = ey + 2


160.

Let f : R  R be a differentiable function and f(1) = 4. Then the value of limx14fx2tx - 1dt, if f'(1) = 2 is :

  • 16

  • 8

  • 4

  • 2


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