Hi I'm a third year physics student currently working on my bachelorstage, and I have a differential equation I want to solve, but can't =). Given an planet with an atmosphere so thick relative to the planet radius, that gravitation in the atmosphere cannot be seen as a constant but decreases with the distance from the planet. I'd say the differential equation for the atmosphere density of a perfect gas would be: [tex] $ Gravitation(r) * \rho * dA = Pressure(r)*d\theta*r - (Pressure + dPressure)*d\theta*(r+dr) $ [/tex] , where dA = ((r+dr)^2-r^2)*PI , Pressure = Constant*rho , and Gravitation(r) = G*PlanetMass/r^2 which can be simplified to: [tex] $ G*PlanetMass/r^2 * \rho * (dr^2+2rdr) * PI = - C*(\rho*dr + d\rho * (r+dr))*d\theta $ [/tex] I guess I can just remove the dr^2 right? Normally I'd try to solve this by bringing both variables to one side of the equation, say rho to the left and r to the right side, and then integrate. But I can't do that now because of the two messy terms on the RHS (right hand side). Any help on this? Maybe I should just neglect some terms in order to make this more easily solvable?