An integrating factor of the differential equationxdydx +&th

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 Multiple Choice QuestionsMultiple Choice Questions

181.

Degree and order of the differential equation d2ydx2 = dydx2 are respectively

  • 1, 2

  • 2, 1

  • 2, 2

  • 1, 1


182.

The solution of the differential equation (1 + y) tan-1(x)dx + y(1 + x2)dy = 0 is

  • logtan-1xx + y1 + x2 = c

  • log1 + y2 + tan-1x2 = c

  • log1 + x2 + logtan-1y = c

  • tan-1x1 + y2 + c = 0


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183.

An integrating factor of the differential equation

xdydx +ylogx = xexx12logx, (x > 0), is

  • xlogx

  • xlogx

  • elogx2

  • ex2


C.

elogx2

Given differential equation is

xdydx +ylogx = xexx12logxor dydx + y . 1xlogx = ex x- 12logxHere, P = 1xlogx and Q = ex x- 12logx

 IF = e1xlogxdx         = elogx22 = elogx2


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184.

Solution of the differential equation

dydxtany = sinx + y + sinx - y

  • secy + 2cosx = c

  • secy - 2cosx = c

  • cosy - 2sinx = c

  • tany - 2secy = c


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185.

The order of the differential equation whose solution is y = a cos(x) + b sin(x) + ce-x , is

  • 3

  • 1

  • 2

  • 4


186.

The differential equation of all parabolas with axis parallel to the axis of y is

  • y2 = 2y1 + x

  • y3 = 2y1

  • y23 = y1

  • None of these


187.

The solution of the differential equation dydx = x - y + 32x - y + 5 is

  • 2x - y + logx - y = x + c

  • 2x - y - logx - y + 2 = x + c

     

  • 2x - y + logx - y + 2 = x + c

  • None of the above


188.

The solution of the differential equation (3.xy + y2)dx + (x2 + xy)dy = 0 is

  • x2(2xy + y2) = c2

  • x2(2xy - y2) = c2

  • x2(y2 - 2xy) = c2

  • None of these


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189.

The order and degree of the differential equation dydx - 4dydx - 7x = 0 are

  • 1 and 1/2

  • 2 ana 1

  • 1 and 1

  • 1 and 2


190.

General solution of the differential equation 

dydx = x + y + 1x + y - 1 is given by

  • x + y = logx + y + c

  • x - y = logx + y + c

  • y = x + logx + y + c

  • y = xlogx + y + c


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