y + x2 =dydx has the solution from Mathemati

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 Multiple Choice QuestionsMultiple Choice Questions

331.

The solution of the differential equation 1 + y2 + x - etan-1ydydx = 0 is given by

  • x - 2 = ketan-1y

  • 2xetan-1y = e2tan-1y + k

  • xetan-1y = tan-1y + k

  • xetan-1y = etan-1y + k


332.

The integrating factor of the differential equation dydx + yx = x3 - 3 will be

  • x

  • log(x)

  • - x

  • ex


333.

The solution of xdx + ydy = x2ydy - xy2dx is

  • x2 - 1 = C(1 + y2)

  • x2 + 1 = C(1 - y2)

  • x2 - 1 = C(1 - y2)

  • x2 + 1 = C(1 - y2)


334.

The solution of x2 + y2dydx = 4 is

  • x2 + y2 = 12x + C

  • x2 + y2 = 3x + C

  • x2 + y2 = 8x + C

  • x3 + y3 = 12x + C


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335.

The solution of dydx + y = ex is

  • 2y = e2x + C

  • 2yex = ex + C

  • 2yex = e2x + C

  • 2ye2x = 2ex + C


336.

Order of the differential equation of the family of all concentric circles centered at (h, k) is

  • 1

  • 2

  • 3

  • 5


337.

The solution of dydx + 13y = 1 is

  • y = 3 + cex3

  • y = 3 + ce - x3

  • 3y = c + e x3

  • y2 + x + x2 + 2 = ce2x


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338.

y + x2 =dydx has the solution

  • y + x2 + 2x + 2 = cex

  • y + x + 2x2 + 2 = cex

  • y2 + x + x2 + 2 = ce2x

  • y + x + x2 + 2 = ce2x


A.

y + x2 + 2x + 2 = cex

We have,      y + x2 = dydxdydx - y = x2It is a linear differential equation. On compairing with dydx + Py = Q, we getP = - 1, Q = x2IF = epdx = e - 1dx = e - xRequired solution isye - x = x2e - xdx + cye - x = x2e - x + 2xe - xdxye - x = -x2e - x - 2xe - x + 2xe - xdxye - x = -x2e - x - 2xe - x -  2e - x + c        y = - x2 + 2x + 2 + cex y + x2 + 2x + 2 = cex


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339.

The solution of dydx = xy - 13 is

  • x23 + y23 = c

  • y23 - x23 = c

  • x13  +  y13 = c

  • y13 - x13 = c


340.

The differential equation of the family of parabola with focus as the origin and the axis as X-axis, is

  • ydydx2 + 4xdydx = 4y

  • - ydydx2 = 2xdydx - y

  • ydydx2 + y = 2xydydx

  • ydydx2 + 2xydydx + y = 0


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