The  solution  of  the  d

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 Multiple Choice QuestionsMultiple Choice Questions

1.

What is the general solution of the differential equation dydx + xy = 0 ?

  • x2 + y2 = c

  • x2 - y2 = c

  • x2 + y2 = cxy

  • x + y = c


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2.

The  solution  of  the  differential  equation dydx = cosy - x + 1 is : 

  • exsecy - x - tany - x = c

  • exsecy - x + tany - x = c

  • exsecy - xtany - x = c

  • ex = csecy - x + tany - x


D.

ex = csecy - x + tany - x

We have, dydx = cosy - x +1   dydx - 1 = cosy - xLet y - x = t  dydx - 1 = dtdx     dtdx = cott    dtcost = dx   sectdt = dxTaking Integration of both side, we getsect . dt = dxlogsect + tant = x + c1Where c1 is a constant       sect + tant = ex + c1       sect + tant = ex . ec11ecsect + tant = exWhere 1ec is a constantcsecy - x + tany - x = ex


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3.

If y = acos2x + bsin2x, then :

  • d2ydx2 + y = 0

  • d2ydx2 + 2y = 0

  • d2ydx2 -4y = 0

  • d2ydx2 + 4y = 0


4.

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

  • x2 + y2 - 2xydydx = 0

  • x2 + y2 +2xydydx = 0

  • x2 - y2 + 2xydydx = 0

  • x2 - y2 - 2xydydx = 0


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5.

Consider the following in respect of the differential equation : 

d2ydx2 + 2dydx2 + 9y = x

  1. The degree of the differential equation is 1.
  2. The order of the differential equation is 2.

Which of the above statements is/are correct?

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


6.

What is the solution xdy - ydx = 0 ?

  • xy = c

  • y = cx

  • x + y = c

  • x - y = c


7.

The order and degree of the differential equation y2  = 4a(x - a), where 'a'· is an arbitrary constant, are respectively : 

  • 1, 2

  • 2, 1

  • 2, 2

  • 1, 1


8.

Which one of the following differential equations has a periodic solution ?

  • d2xdt2 + μx = 0

  • d2xdt2 - μx = 0

  • xdxdt + μt = 0

  • dxdt + μxt = 0


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9.

If y = ex2sin2x, then what is dydx at x = π equal to ?

  • 1 + πeπ2

  • 2πeπ2

  • 2eπ2

  • eπ2


10.

What is the solution of :

(1 + 2x)dy - (1 - 2y)dx = 0 ?

  • x - y - 2xy = c

  • y - x - 2xy = c

  • y + x - 2xy = c

  • x + y + 2xy = c


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