If xsinxydy = ysinyx - xdx and 

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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


C.

logx

xsinxydy = ysinyx - xdx dydx = ysinyx - xxsinyx = yxsinyx - 1sinyxLet yx = u and dydx = xdudx + u    xdudx + u = usinu - 1sinu           xdudx = usinu - 1 - usinusinu - sinudu = 1xdx

On integrating both sides, we get

        cosu = logx + c cosyx = logx + c        y1 = π2 cosπ2 = log1 + c      c = 0Thus, cosyx = logx


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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


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


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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