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

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Show that the differential equation representing the family of curves y2 = 2a(x + a2/3) where a is a positive parameter, is (y2 - 2xy(dy/dx))3 = 8(y(dy/dx))5.

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Given equation is y2 = 2a(x + a2/3), a is the parameter.

y2 = 2ax + 2 a5/3 ... (1) 

Differentiating with respect to x 

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