Particular Solution to General Solution of a Differential Equation I had to find the general solution of the differential equation of $dp/dh = -Kp$. My solution is $p=Ae^{-Kh}$. Now I need to find the particular solution that describes the pressure of the atmosphere $(p)$ as a function of height $(h)$. I am also told that the pressure at sea level is $103100$Pa.
My solution: The given differential equation is similar to that for the exponential model for radioactive decay. So by comparison to that model, the differential equation has the general solution
$$p = p_0 e^{-Kh} $$
$$103100 = p_0 e^{-Kh}.$$
Am I correct, thanks.

At sea level, $h=0$ and $p=103100$Pa. Putting this in $p=Ae^{-Kh}$, we get, $A=103100$. So, the particular solution becomes $p=103100e^{-Kh}$.
Or in your working, it's $p_0=103100$. Particular solution or general solution should include variable, which is $p$ here.
