Consider the first order separable equation $y^{\text{'}}=\frac{16}{3}xy(1+2x^2{)}^{\frac{1}{3}}$

An explicit general solution can be written in the form $y=Cf(x)$ for some function $f(x)$ with $C$ an arbitrary constant. Here $f(x)=$

Next find the explicit solution of the initial value problem $y(0)=2$

$y=$

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