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Question

The differential equation ydx +y2dy = xdy and y(1) = 1 represents a parabola whose


A

Vertex is (0, 0)

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B

axis is x = 1

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C

length of latus rectum is 4

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D

tangent at the vertex is x = 1

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Solution

The correct option is D

tangent at the vertex is x = 1


Given equation

ydxxdyy2 + dy = 0

xy + y = c,

but y(1) = 1 c = 2

xy + y = 2

x + y2 = 2y

(y1)2 = - (x-1)


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