Problem

(a) Given that $y=1$ at $x=0$, solve the differential equation

$$\frac{dy}{dx}=\frac{6xy^{1/3}}{e^{x^2}}\qquad y\geq 0$$

giving your answer in the form $y^2=g(x)$.

(b) Hence find the equation of the horizontal asymptote to the curve with equation $y^2=g(x)$.