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User:Tohline/Math/EQ RadialPulsation03

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~0 = 
\frac{d^2x}{d\xi^2} + \biggl[4 - \xi \biggl( \frac{d\psi}{d\xi} \biggr) \biggr] \frac{1}{\xi} \cdot \frac{dx}{d\xi} 
+  \biggl[ \biggl( \frac{\sigma_c^2}{6\gamma_\mathrm{g}}\biggr)\xi^2 - \alpha \xi \biggl( \frac{d\psi}{d\xi} \biggr)   \biggr]  \frac{x}{\xi^2}

where:    ~\sigma_c^2 \equiv \frac{3\omega^2}{2\pi G\rho_c}     and,     ~\alpha \equiv \biggl(3 - \frac{4}{\gamma_\mathrm{g}}\biggr)

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