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Cake day: July 1st, 2023

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  • I’m not into meteorology, so I’ll just assume the previous steps are correct and jump to the differential equation.

    This is a 1st order DE, meaning that it only contains the first derivative of the function, which is the easiest case. If I’m doing it correctly, the solution is in the form P = Ae^(-hg/(R*T)), where e is Euler’s number, and A is a constant that you have to determine from something other than the equation (because any constant would work as far as the math is concerned). In this case, you should can set A equal to the pressure at the surface, so that the solution gives you that same value for h=0, and an exponentially decreasing pressure as the height increases.