0 = \frac{\partial F}{\partial f} + \frac{\partial G}{\partial f} + 2\pi r p -  \frac{d}{dr}(\frac{\partial F}{\partial f'}) - \frac{d}{dr}(\frac{\partial G}{\partial f'}) + \frac{d^2}{dr^2}(\frac{\partial G}{\partial f''})