The solution of dydx = ax + hby +&n

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 Multiple Choice QuestionsMultiple Choice Questions

161.

The solution of dydx + y tan(x) = sec(x) is :

  • ysecx = tanx + c

  • ytanx = secx + c

  • tanx = ytanx + c

  • xsecx = tany + c


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162.

The solution of dydx = ax + hby + k represents a parabola, when :

  • a = 0, b = 0

  • a = 1, b = 2

  • a = 0, b  0

  • a = 2, b = 1


C.

a = 0, b  0

The given differential equation is

                 dydx = ax + hby + kOn integrating both sides. by + kdy = ax + hdx by22 + ky = ax22 + hx + c

Thus, above equation represents a parabola, if a = 0 and b ≠ 0


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163.

An integrating factor of the differential equation xdydx + ylogx = xexx12logx, (x > 0) is :

  • xlog(x)

  • xlogx

  • elogx2

  • ex2


164.

The solution of edydx = x + 1, y(0) = 3 is :

  • y = xlog(x) - x + 2

  • y = (x + 1)logx + 1 - x + 3

  • y = x + 1logx + 1 + x + 3

  • y = xlogx + x + 3


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165.

Solution of the differential equation dydxtany = sinx + y + sinx - y is :

  • secy + 2cosx = c

  • secy - 2cosx = c

  • cosy - 2sinx = c

  • tany - 2secy = c


166.

Solution of the differential equation dydx + yx = sinx is :

  • xy + cosx = sinx + c

  • xy - cosx = sinx + c

  • xycosx = sinx + c

  • xy - cosx = cosx + c


167.

The solution of the differential equation xdydx + 2y = x2 is :

  • y = x2 + c4x2

  • y = x24 + c

  • y = x2 + cx2

  • y = x4 + c4x2


168.

y = - A cos(5x) + B sin(5x) satisfies the differential equation :

  • d2ydx2 + 10dydx + 25y = 0

  • d2ydx2 - 10dydx + 25y = 0

  • d2ydx2 - 25y = 0

  • d2ydx2 + 25y = 0


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169.

The order and degree of the differential equation sinxdx + dy = cosxdx - dy is :

  • (1, 2)

  • (2, 2)

  • (1, 1)

  • (2, 1)


170.

An integrating factor of the differential equation, (1 + y + x2y)dx + (x + x3)dy = 0 is :

  • logx

  • x

  • ex

  • 1x


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