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in Differential Equations by (28.2k points)
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(i) Choose the correct answer from the bracket. The solution of the differential equation xdy + ydx = 0 represents

(a) a rectangular hyperbola

(b) a parabola whose centre is origin

(c) a straight line whose centre is origin

(d) a circle whose centre is origin.

(ii) From the DE of the family of circles touching the x-axis at origin.

1 Answer

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Best answer

(i) (c) a straight line whose centre is origin.

(ii) Let (0, a) be the centre of the circle. Therefore the equation of the circle is

x2 + (y – a)2 = a2

⇒ x2 + y2 = 2ay

⇒ \(\frac{x^2+y^2}{y}\) = 2a ____(1)

Differentiating with respect to x,

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