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

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Neil Smith on 13 Feb 2020
Edited: Neil Smith on 24 Jan 2021
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.

Deepak Meena on 22 Jan 2021
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 on 24 Jan 2021
Edited: Neil Smith on 24 Jan 2021
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...

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