Let us cosider an infinite (in x and y) static isothermal slab, symmetric about z = 0, supported by gas pressure and under it's own gravity. No other forces are acting. To calculate the density distribution as a function of z.
Notice that since the slab is infinite in x and y, $\nabla = \del/{\del z }$ and the density and the gravitational potential $\psi$ are function of z only.
I was thinking to start with the force by gas pressure and force by gravity. But how to start and solve I am stuck.
I request valuable suggestions to solve this problem. Thanks!