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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?

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maybe you wanted to type $\ln(1)=0$ –  Evgeny Savinov Feb 5 '12 at 21:32

1 Answer 1

Hint: you need $\ln(\theta)$ to be defined, and you also can't let the denominator be $0$.

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