deletions | additions       diff --git a/initialwindtemperature.tex b/initialwindtemperature.tex  index ec2c4a6..643adec 100644  --- a/initialwindtemperature.tex  +++ b/initialwindtemperature.tex 
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P(z) & = & \rho_0 v_0^2 + \rho_0 \frac{k T_0}{\mu m_{\textrm{H}}} \nonumber\\   & = & \frac{\dot{M}}{4\pi v_{\infty}(z^2+\omega^2)} \left( v_{\infty}^2 \sin^2(\psi) + \frac{kT}{\mu m_{\textrm{H}}}\right)\\  \end{eqnarray}  and thus eqn.~\label{eqn:ode} eqn.~\ref{eqn:ode}  becomes \begin{equation}  \frac{\rm{d}\omega}{\rm{d}z} = \tan\left[\arctan\left(\frac{\omega}{z}\right)-\arcsin\sqrt{\frac{z^2+\omega^2}{R_0^2}-\frac{kT}{\mu m_{\textrm{H} v_infty^2}}}\right]\ .  \end{equation}