Symbolic Integration of two functions that are the gradient of a function

Is it possible to get matlab to do a symbolic integration of a gradient where you know that each term is dependent only on one variable?

I'm trying to get Matlab to do the following:

syms P(r,z) rho g omega P_atm
ode1 = diff(P,z) == rho * g
ode2 = diff(P,r) == rho * omega^2 / r

ode_total = ode1 + ode2
cond = P(0,0) = P_atm

soln(r,z) = dsolve(ode_total, cond);

Essentially, I'm trying to do the following:

Given the following pressure gradient in two dimensions (or three, where ), solve for the pressure as a function of r and z [and θ]:

,

using the relation: and boundary condition:

How do I code the above process to result in the following solution (or is it even possible)?

As you might have guessed, these equations are derived from navier-stokes.

Answer 1

[Deepak Meena]

Hi Neil,

I think on the line no 7 you meant :

cond = P(0,0) == P_atm

Now coming to your question dsolve is used to solve differential equation with one independent variable.

To Solve partial differntial equation I advised you to use pdepe()

[Neil Smith]

I think I ended up taking a different approach to get it working. I finished that course 9 months ago, so I don't remember, now...

Thanks for your response, anyway