
\begin{enumerate}
\item $y' + 3y = -5 \iff y' = -3y - 5 \iff y(x)=C\e^{-3x} - \dfrac{-5}{-3}= \boxed{ C\e^{-3x}-\dfrac{5}{3}\quad,\quad C\in\R}$.

\item $3y' + 2y = 1 \iff y' = -\dfrac{2}{3}y + \dfrac{1}{3} \iff y(x) = C\e^{-\frac{2}{3}x} - \dfrac{1/3}{-2/3} = \boxed{ C\e^{-\frac{2}{3}x} + \dfrac{1}{2}\quad,\quad C\in\R}$.

\item $y = y'+3 \iff y' = y-3 \iff y(x) = C\e^{x}-\dfrac{-3}{1} = \boxed{C\e^{x}+3\quad,\quad C\in\R}$.
\end{enumerate}
