MATLAB: How to solve ODE with symbolic conditions

conditionsdsolvesymbolicSymbolic Math Toolbox

Hello,
I have an issue with the boundary conditions for this ODE. With the code as is it assumes that Dw is a function of a not that for r it should subsitute a. How can I solve this?
clear; clc;
syms a P G t nu F Q r D w(r)
F = - pi * a^2 * P
Q = (pi*r^2*P) / (2*pi*r)
ode = diff(((1/r)*diff((r*diff(w,r)),r)),r) == Q/D
Dw = diff(w,r);
cond1 = Dw(0) == 0
cond2 = Dw(a) == 0
cond3 =  w(a) == 0
conds = [cond1 cond2 cond3];
wSol(r) = dsolve(ode,conds)
In all I try to solve this ODE:
with the following 3 BC:
Thank you,

Best Answer

Hi,
I tried to solve the differential equation with the given code and I see that the returned wSol(r) is a function of r only and not a. Also, DW too is a function of r if you check in the workspace about the independent variable present for DW. I checked the solution too and it looks correct to me.
This is the solution I got. 
wSol(r) = (P*a^4 - 2*P*a^2*r^2 + P*r^4)/(64*D);
You may want to check again about the correctness of the solution.
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