0 = d 2 x d ξ 2 + [ 4 − ξ ( d ψ d ξ ) ] 1 ξ ⋅ d x d ξ + [ ( σ c 2 6 γ g ) ξ 2 − α ξ ( d ψ d ξ ) ] x ξ 2 {\displaystyle 0={\frac {d^{2}x}{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: σ c 2 ≡ 3 ω 2 2 π G ρ c {\displaystyle \sigma _{c}^{2}\equiv {\frac {3\omega ^{2}}{2\pi G\rho _{c}}}} and, α ≡ ( 3 − 4 γ g ) {\displaystyle \alpha \equiv {\biggl (}3-{\frac {4}{\gamma _{\mathrm {g} }}}{\biggr )}}
and, 
![{\displaystyle 0={\frac {d^{2}x}{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}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef1df66d8b54b33bf4753ec7261b1cf5605af438)