Originally Posted by

**dankelly07** Just need a bit of help finishing this one, not sure if I'm going about this correctly...

$\displaystyle

\begin{gathered}

\frac{{dy}}

{{dx}} = \frac{{y^2 + 3xy + x^2 }}

{{x^2 }} \hfill \\

\frac{{dy}}

{{dx}} = \frac{{v^2 + 3v}}

{x} - \frac{v}

{x} \hfill \\

\frac{{dy}}

{{dx}} = v^2 + 2v/x \hfill \\

\hfill \\

\int {\frac{{dv}}

{{v(v + 2v)}} = \int {\frac{{dx}}

{x} = > \int {(\frac{1}

{v} - \frac{1}

{{1 + v}})dv = \int {\frac{{dx}}

{x}} } } } \hfill \\

\end{gathered}

$

$\displaystyle

\ln |v/2 + v| = \ln |x| + A

$

......

I need to know how to get to this....

$\displaystyle

\frac{x}

{{A - \ln |x|}} - x

$