The general solution of the differential equationd2ydx2 +&nb

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 Multiple Choice QuestionsMultiple Choice Questions

91.

The solution of the differential equation dydx = sinx + ytanx +y - 1 is

  • cscx +y + tanx + y = x +c

  • x + cscx + y = c

  • x + tanx + y = c

  • x + secx + y = c


92.

The differential equation of all straight lines touching the circle x2 + y2 = a2 is

  • y - dydx2 = a21 + dydx2

  • y - xdydx2 = a21 + dydx2

  • y - xdydx = a21 + dydx

  • y - dydx = a21 - dydx


93.

The differential equation dydx + y + 3 = 0 admits

  • infinite number of solutions

  • no solutions

  • a unique solution

  • many solutions


94.

Solution of the differential equation xdy - ydx - x2 + y2dx = 0

  • y - x2 + y2 = cx2

  • y + x2 + y2 = cx2

  • y + x2 + y2 = cy2

  • x - x2 + y2 = cy2


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95.

If xsinxydy = ysinyx - xdx and y1 = π2, then the value of cosyx is equal to :

  • x

  • 1x

  • logx

  • ex


96.

The differential equation of the system of all circles of radius r in the xy plane is :

  • 1 + dydx32 = r2d2ydx22

  • 1 + dydx32 = r2d2ydx23

  • 1 + dydx23 = r2d2ydx22

  • 1 + dydx23 = r2d2ydx23


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97.

The general solution of the differential equation

d2ydx2 + 2dydx + y = 2e3x is given by

  • y = c1 + c2xex + e3x8

  • y = c1 + c2xe- x + e- 3x8

  • y = c1 + c2xe- x + e3x8

  • y = c1 + c2xex + e- 3x8


C.

y = c1 + c2xe- x + e3x8

The equation can be written as

(D2 + 2D + 1)y = 2e3x, where ddx = D

Here, F(D) = D2 + 2D + 1 and Q = 2e3x

The auxillary equation is

m2 + 2m + 1 = 0  (m + 1)2 = 0

             m = - 1, - 1

 The CF = c1 + c2xe- x

and PI = 1FD2e3x = 2 . 1D2 + 2D + 1 . e3x           = 2 . e3x9 + 6 + 1 = e3x8

Hence, the complete solution is

     y = CF + PI

 y = c1 + c2xe- x + e3x8


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98.

The solution of the differential ydx + (x - y3)dy = 0 is:

  • xy = 13y3 + c

  • xy = y4 + c

  • y4 = 4xy + c

  • 4y = y3 + c


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99.

If the distances covered by a particle in time t is proportional to the cube root of its velocity, then the acceleration is

  • a constant

  •  s3

  •  1s3

  •  s5


100.

The solution of the differential equation dydx = yx + ϕyxϕ'yx is

  • yx = k

  • ϕyx = kx

  • yx = k

  • ϕyx = ky


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