The differential equation for, which y = a cos(x) + b sin(x) is a

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 Multiple Choice QuestionsMultiple Choice Questions

141.

The general solution of the differential equation xdy - ydx = y2dx is

  • y = xC - x

  • x = 2yC + x

  • y = C + x2x

  • y = 2xC + x


142.

The order of the differential equation d3ydx32 + d2ydx22 + dydx5 = 0 is

  • 3

  • 4

  • 1

  • 5


143.

The solution of dy/dx + ytan(x) = sec(x), y(0) = 0 is

  • ysec(x) = tan(x)

  • ytan(x) = sec(x)

  • tan(x) = ytan(x)

  • xsec(x) = tan(y)


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144.

The differential equation for, which y = a cos(x) + b sin(x) is a solution, is :

  • d2ydx2 + y = 0

  • d2ydx2 - y = 0

  • d2ydx2 + a + by = 0

  • d2ydx2 = a + by


A.

d2ydx2 + y = 0

Given,        y = acosx + bsinxOn differentiating w.r.t. x, we get               dydx = - a sinx + b cosxAgain differentiating, we get             d2ydx2 = - acosx - bsinx                     = - acosx + bsinx = - y d2ydx2 + y = 0


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145.

The solution of dydx + Pxy = 0 is

  • y = cePdx

  • y = ce- Pdx

  • x = ce- Pdy

  • x = cePdy


146.

The differential equation of the family of lines passing through the origin is :

  • xdydx + y = 0

  • x + dydx = 0

  • dydx = y

  • xdydx - y = 0


147.

The solution of dydx + y = e- x; y(0) = 0 is :

  • y = e- x(x - 1)

  • y = xe- x

  • y = xe- x + 1

  • y = (x + 1)e-x


148.

The degree of the differential equation d2ydx2 + dydx3 + 6y = 0 is :

  • 1

  • 3

  • 2

  • 5


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149.

The solution of the equation (2y - 1)dx - (2x + 3)dy = 0 is  :

  • 2x - 12y + 3 = c

  • 2x + 32y - 1 = c

  • 2x - 12y - 1 = c

  • 2y + 12x - 3 = c


150.

Let F denotes the family of ellipses whose centre is at the origin and major axis is the y-axis. Then, equation of the family F is :

  • d2ydx2 + dydxxdydx - y = 0

  • xyd2ydx2 + dydxxdydx - y = 0

  • xyd2ydx2 + dydxxdydx - y = 0

  • d2ydx2 - dydxxdydx - y = 0


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