Problem source

\begin{questionparts}
\item Solve the differential equation 
\[
\frac{\mathrm{d}y}{\mathrm{d}x}-y-3y^{2}=-2
\]
by making the substitution $y=-\dfrac{1}{3u}\dfrac{\mathrm{d}u}{\mathrm{d}x}.$

\item Solve the differential equation 
\[
x^{2}\frac{\mathrm{d}y}{\mathrm{d}x}+xy+x^{2}y^{2}=1
\]
by making the substitution 
\[
y=\frac{1}{x}+\frac{1}{v},
\]
where $v$ is a function of $x$. 
\end{questionparts}