(3,-1) is the intersection between two lines right?
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Well, what I would do is let:
$\displaystyle w=\frac{v}{u}\implies v=uw\implies \frac{dv}{du}=w+u\frac{dw}{du}$
And so our ODE becomes:
$\displaystyle w+u\frac{dw}{du}=\frac{1+2w}{2+w}$
$\displaystyle u\frac{dw}{du}=\frac{1+2w-w(2+w)}{2+w}$
$\displaystyle u\frac{dw}{du}=\frac{1-w^2}{2+w}$
Can you proceed?