The family of curves y = easin(x), where a is anarbitrary constan

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 Multiple Choice QuestionsMultiple Choice Questions

111.

The integrating factor of the differential equation ylogydx = logy - xdy is

  • 1logy

  • loglogy

  • 1 + logy

  • logy


112.

The solution of the differential equation dydx = 1x + y2 is

  • y = - x2 - 2x - 2 + cex

  • y = x2 + 2x + 2 - cex

  • x = - y2 - 2y + 2 - cey

  • x = - y2 - 2y - 2 + cey


113.

The solution of the equation 3 + 22x2 - 8 + 3 + 228 - x2 = 6 are

  • 3 ± 22

  • ± 1

  • ± 33, ± 22

  • ± 3, ± 7


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114.

The family of curves y = easin(x), where a is anarbitrary constant, is represented by thedifferential equation 

  • logy = tanxdydx

  • ylogy = tanxdydx

  • ylogy = sinxdydx

  • logy = cosxdydx


B.

ylogy = tanxdydx

Given curve is

y = easin(x)            ...(i)

Taking log on both sides, we get

log(y) = a sin(x)    ...(ii)

Differentiating w.r.t. x, we get

1y dydx = a cosx   ...(iii)

Dividing Eq. (iii) by Eq. (ii), we get

       1y dydxlogy = a cosxa sinx        dydx = y logy cotx x logy = tanx dydx


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115.

The integrating factor of x dydx + 1 + x y = x is

  • x

  • 2x

  • exlog(x)

  • xex


116.

The solution of the differential equation dydx + 1 = ex + y is

  • x + ex + y = c

  • x - ex + y = c

  • x + e- (x + y) = c

  • x - e- (x + y) = c


117.

The degree and order of the differential equation y = px + a2p2 + b23, where p = dydx, are respectively.

  • 3, 1

  • 1, 3

  • 1, 1

  • 3, 3


118.

The differential equation representing the family of curves y2 = 2c (x + c) where c is a positive parameter, is of

  • order 1, degree 2

  • order 1, degree 3

  • order 2, degree 3

  • order 2, degree 2


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119.

An integrating factor of the differential equation 1 + x2dydx + xy = x is

  • x1 + x2

  • 12log1 + x2

  • 1 + x2

  • x


120.

The solution of the differential equation xdydx + y = 1x2 at (1, 2) is

  • x2y + 1 = 3x

  • x2y + 1 = 0

  • xy + 1 = 3x

  • x2(y + 1) = 3x


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