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Show that the differential equation representing the family of curves `y^(2)=2a(x+a^((2)/(3)))` where a is positive parameter, s `(y^(2)-2xy(dy)/(dx))^(3)=8(y(dy)/(dx))^(5)`

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The correct Answer is:
`(y^(2)-2xy(dy)/(dx))^(3)=8(y(dy)/(dx))^(5)`
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