The differential equation representing a family of circles touchm

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 Multiple Choice QuestionsMultiple Choice Questions

241.

The general solution of the differential equation dydx +  1 + cos2y1 - cos2y = 0 is given by

  • tany + cotx = c

  • tany - cotx = c

  • tanx - coty = c

  • tanx + coty = c


242.

The degree of the differential equation 1 + dydx234 = d2ydx213 is

  • 2

  • 4

  • 9

  • 1


243.

The differential equation for which sin-1(x) + sin-1(y) = c is given by

  • 1 - x2dy + 1  - y2dx = 0

  • 1 - x2dx + 1  - y2dy = 0

  • 1 - x2dx - 1  - y2dy = 0

  • 1 - x2dy - 1  - y2dx = 0


244.

The differential of ex3 with respect to log(x) is

  • ex3

  • 3x2ex3 + 3x2

  • 3x2ex3

  • 3x3ex3


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245.

Which of the following functions is a solution of the differential equation ?

dydx2 - xdydx + y = 0

  • y = 2x - 4

  • y = 2x2 - 4

  • y = 2

  • y = 2x


246.

y = aemx + be- mx satisfies which of the following differential equations

  • dydx + my = 0

  • dydx - my = 0

  • d2ydx2 - m2y = 0

  • d2ydx2 + m2y = 0


247.

Solution of the differential equation dxx + dyy = 0 is

  • 1x + 1y = c

  • log(x)log(y) = c

  • xy = c

  • x + y = c


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248.

The differential equation representing a family of circles touchmg the Y-axis at the origin is

  • x2 +y2 - 2xydydx = 0

  • x2 +y2 + 2xydydx = 0

  • x2 -y2 - 2xydydx = 0

  • x2 -y2 + 2xydydx = 0


D.

x2 -y2 + 2xydydx = 0

Since, the circle touches the Y-axis, therefore the centre lies on the X-axis. Let the centre be (h,0).

 Radius of circle = h The equation of circle is given byx - h2 + y - 02 = h2    x2 +y2 - 2hx = 0      ...iOn differentiating both sides w.r.t x, we get2x +2ydydx - 2h = 0 h = x + ydydxPutting the value of h in Eq. (i), we get x2 +y2 - 2xx + ydydx = 0  - x2 +y2 - 2xydydx = 0     x2 - y2 + 2xydydx = 0This is the required differential equation.


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249.

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

  • x+ y2 + xy - x + y = c

  • x+ y2 - xy + x + y = c

  • x2 - y2 + xy - x + y = c

  • x2 - y2 - xy + x + y = c


250.

The solution of the differential equation e-x(y + 1)dy + (cos2(x) + sin(2x))y dx = 0 subjected to the condition that y = 1 when x = 0 is

  • y + log(y) + excos2(x) = 2

  • log(y + 1) + excos2(x) = 1

  • y + log(y) = excos2(x)

  • (y + 1) + excos2(x) = 2


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