The general solution of the differential equation x +&n

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 Multiple Choice QuestionsMultiple Choice Questions

131.

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

  • y = e+ C

  • y = x + ex + C

  • y = xex + C

  • y = x(ex + 1) + C


132.

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

  • 1, 1

  • 1, 2

  • 1, 3

  • 2, 2


133.

An integrating factor of the differential equation sinxdydx + 2ycosx = 1 is

  • sin2(x)

  • 2sinx

  • logsinx

  • 1sin2x


134.

If x2 + y2 = 1, then

  • yy'' + (y')2 + 1 = 0

  • yy'' +2 (y')2 + 1 = 0

  • yy'' - 2(y')2 + 1 = 0

  • yy'' + (y')2 - 1 = 0


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135.

The solution of the differential equation y'(y2 - x) = y is

  • y3 - 3xy = C

  • y3 + 3xy = C

  • x3 - 3xy = C

  • y3 - xy = C


136.

The order and degree of the differential equation 2d2ydx2 + dydx232 = d3ydx3 are respectively

  • 2 and 2

  • 2 and 1

  • 3 and 2

  • 3 and 3


137.

The slope of a curve at any point (x, y) other than the origin, is y + yx. Then, the equation of the curve is

  • y = C xex

  • y = x(ex + C)

  • xy = Cex

  • y + xex = C


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138.

The general solution of the differential equation x + y + 3dydx = 1 is

  • x + y + 3 = Cey

  • x + y + 4 = Cey

  • x + y + 3 = Cey

  • x + y + 4 = Cey


B.

x + y + 4 = Cey

We have, x + y + 3dydx = 1 x + y + 3 = dxdy     ...iLet   x + y + 3 = tOn differentiating w.r.t.y, we getdxdy + 1 = dtdy  dtdy = t + 1      from Eq. (i), t = dxdyOn integrating both sides,                 logt + 1 = y + C1 logx + y + 3 + 1 = y + C1                x + y + 4 = Cey                where, c = eC1


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139.

The differential equation representing the family of curves y2 = a(ax + b), where a and b are arbitrary constants, is of

  • order 1, degree 1

  • order 1, degree 3

  • order 2, degree 3

  • order 2, degree 1


140.

The solution of the differential equation xdydx - yx2 - y2 = 10x2 is

  • sin-1yx - 5x2 = C

  • sin-1yx = 10x2 + C

  • yx = 5x2 + C

  • sin-1yx = 10x2 + Cx


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