8. (a) Given that \(y = 1\) at \(x = 0\), solve the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 6 x y ^ { \frac { 1 } { 3 } } } { \mathrm { e } ^ { 2 x } } \quad y \geqslant 0$$ giving your answer in the form \(y ^ { 2 } = \mathrm { g } ( x )\).
(b) Hence find the equation of the horizontal asymptote to the curve with equation \(y ^ { 2 } = \mathrm { g } ( x )\).
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