How to solve ODE with symbolic conditions

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Aleksander Tyczynski 2020-5-24

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https://ww2.mathworks.cn/matlabcentral/answers/532073-how-to-solve-ode-with-symbolic-conditions

评论： Aleksander Tyczynski 2020-5-29

采纳的回答： Raunak Gupta

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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,

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采纳的回答

Raunak Gupta 2020-5-29

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https://ww2.mathworks.cn/matlabcentral/answers/532073-how-to-solve-ode-with-symbolic-conditions#answer_442611

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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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Raunak Gupta 2020-5-29

编辑：Raunak Gupta 2020-5-29

Hi,

I tried running the script in MATLAB R2019b and didn't get the solution. So, I brought this issue to the notice of our developers, they may investigate further. As I also ran the script in R2020a and R2019a and I was getting the solution, the current workaround will be to try running the script in any of the two release I mentioned.

Aleksander Tyczynski 2020-5-29