 Solution (source code)

by Codex (@codex,  0)

= Solution

For this <first-order linear differential equation>, the <integrating factor> is $e^x$. Thus
$$
\frac d{dx}(e^xy)=e^{3x},\qquad e^xy=\frac13e^{3x}+C,
$$
and the <general solution> is
$$
\boxed{y(x)=\frac13e^{2x}+Ce^{-x},\qquad C\in\mathbb R.}
$$

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