The differential equation representing the family of curves y = x

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 Multiple Choice QuestionsMultiple Choice Questions

101.

If the integrating factor of the differential equation dydx + Pxy = Qx is x, then P(x) is

  • x

  • x2/2

  • 1/x

  • 1/x2


102.

If c1, c2, c3, c4, c5 and c6  are constants, then the order of the differential equation whose general solution is given by y = c1 cos(x + c2) + c3 sin(x + c4) + c5ex + c6, is

  • 6

  • 5

  • 4

  • 3


103.

y = 2e2x - e- x is solution of the differential equation

  • y2 + y1 + 2y = 0

  • y2 - y1 + 2y = 0

  • y2 + y1 = 0

  • y2 - y1 - 2y = 0


104.

If xdy = y(dx + y dy), y(1) = 1 and y(x) > 0, then y(- 3) is equal to

  • 3

  • 2

  • 1

  • 0


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105.

The differential equation representing the family of curves y = 2c (x + c3), where c is a positive parameter, is of

  • order 1, degree 1

  • order 1, degree 2

  • order 1, degree 3

  • order 1, degree 4


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106.

The differential equation representing the family of curves y = xecx (c is a constant) is

  • dydx = yx1 - logyx

  • dydx = yxlogyx + 1

  • dydx = yx1 + logyx

  • dydx +1 = yxlogyx


C.

dydx = yx1 + logyx

Given, y = xecxOn differentiating w.r.t. x, we getdydx = ecx . c = yx + y . c y = xecx  logy = logx + cx logyx = cx dydx = yx + yxlogyx           = yx1 + logyx


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107.

The solution of dydx = 1 + y + y2 + x + xy + xy2 is

  • tan-12y + 13 = x + xy + xy2

  • 4tan-12y + 13 = 322x + x2

  • 3tan-13y + 13 = 41 +x +x2 + c

  • tan-12y + 13 = 32x + x2 + c


108.

The integrating factor of the differential equation

dydx + y1 - xx = 1 - x is

  • 1 - x1 + x

  • 1 + x1 - x

  • 1 - x1 +x

  • x1 - x


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109.

The solution of cosydydx = ex + siny + x2esiny is

  •  ex - e- siny+ x33 = c

  •  e- x - e- siny+ x33 = c

  •  ex + e- siny+ x33 = c

  •  ex - esiny+ x33 = c


110.

The order and degree of the differential equation

1 + dydx234 = d2ydx213

  • (2, 4)

  • (2, 3)

  • (6, 4)

  • (6, 9)


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