The ODE is $dr/d(\theta)$ = $r^2/\theta,$ $r(1) = 2$
separable equation and integrate both sides: $\int(dr/r^2$ - $\int d\theta/\theta$ =$0$
-$\frac{1}{r} - ln(\theta) = c$
solve for c: $-\frac{1}{2} - ln(1) = c$
-$\frac{1}{2}$ = c
plug back into equation: -$\frac{1}{r} - ln(\theta) = -\frac{1}{2}$
solve for r:
$r = \frac{2}{1-2ln(\theta)}$
My quetion is, how do I find the interval for the solution?