The differential equation dxdy=3y2x represents a family of hyperbolas (except when it represents a pair of lines) with eccentricity

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answer is B.

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Detailed Solution

dxdy=3y2x⇒ ∫2xdx =∫3ydy⇒ x2 =3y22+cor x23−y22=c3 If c is positive, then e=1+23=53If c is negative, then e=1+32=52

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