User:Butakun~enwiki/Taylor-Maccoll equation

In fluid dynamics, Taylor-Maccoll equation is the governing equation for supersonic conical flow, written as

\left(1 - \frac{v^2}{a^2}\right) \frac{d^2 u}{d\theta^2} + \cot\theta\frac{du}{d\theta} + \left(2 - \frac{v^2}{a^2}\right) u = 0 $$

v = \frac{du}{d\theta} $$ where
 * $$u$$ is the velocity component in $$\hat{e}_r$$.
 * $$v$$ is the velocity component in $$\hat{e}_{\theta}$$.
 * $$a$$ is the speed of sound.
 * $$\theta$$ is the semivertex angle.