The solution of the differential equation (1 + y2) dx = (tan-1((y

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 Multiple Choice QuestionsMultiple Choice Questions

311.

The integrating factor of the differential equation xdydx - y = 2x2 is

  • 1x

  • x

  • e-x

  • e-y


312.

If ddxfx = 4x3 - 3x4 such that f(2) = 0. Then, f(x) is

  • x3 + 1x4 - 1298

  • x4 + 1x3 + 1298

  • x3 + 1x4 + 1298

  • x4 + 1x3 - 1298


313.

The order and degree of the differential equation d3ydx32 - 3d2ydx2 + 2dydx4 = y4 are

  • 1, 4

  • 3, 4

  • 2, 4

  • 3, 2


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314.

The solution of the differential equation (1 + y2) dx = (tan-1((y) - x)dy is

  • xetan-1y = (1 - tan-1y)etan-1y + C

  • xetan-1y = (tan-1y - 1)etan-1y + C

  • x = tan-1y - 1 + Cetan-1y

  • None of the above


B.

xetan-1y = (tan-1y - 1)etan-1y + C

Given, differential equation can be written asdxdy + tan-1y - x1 + y2or dxdy + 11+ y2 . x = tan-1y1 + y2It is a linear differential equation of the formdxdy + Px = Qwhere, P = 11 + y2and     Q = tan-1y1 + y2 Integrating factor = ePdy        = e11 + y2dy        = etan-1y Solution isetan-1y . x = etan-1ytan-1y1 + y2dyPut tan-1y = t in right hand side, 11 + y2dy = dt xetan-1y = etII tI dt                        = tet - 1 . etdt + C                        = tet - et + C                        = tan-1y . etan-1y - etan-1y +C xetan-1y = (tan-1y - 1)etan-1y + C


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315.

The solution of the differential equation xdydx = y - xtanyx is

  • xsinxy + C = 0

  • xsiny + C = 0

  • xsinyx = C

  • None of these


316.

The particular solution of cosdydx = awhere, a  R, (y = 2 when x = 0), is

  • cosy - 2x = a

  • siny - 2x = a

  • cos-1x = y + a

  • y = acos-1x


317.

The order and degree of the differential equation d2ydx2 = y + dydx214 are given by

  • 4 and 2

  • 1 and 2

  • 1 and 4

  • 2 and 4


318.

The differential equation of the family of circles touching the y-axis at the origin is

  • xy' - 2y = 0

  • y'' - 4y' + 4y = 0

  • 2xyy' + x2 = y2

  • 2yy' + y2 = x2


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319.

Solution of the equation cos2xdydx - tan2xy = cos2x, x < π4, where yπ6 = 338, is given by 

  • ytan2x1 - tan2x = 0

  • y1 - tan2x = C

  • y = sin2x + C

  • y = 12 sin2x1 - tan2x


320.

The equation of the curve through the point (1, 0), whose slope is y - 1x2 + x, is

  • 2x(y - 1) + x + 1 = 0

  • (x + 1)(y - 1) + 2x = 0

  • x(y - 1)(x + 1) + 2 = 0

  • None of these


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