Solving an equation with integration constants and boundary conditions

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I have issues with solving an equation with integration constants and boundary conditions.
In this case the equation is presented in the image below, where I calculated the problem by my hand and I would like to replicate a similar solution, where I get as a symfun depending on r, and then using vpa to get a numerical value for a specific r, .
Boundary conditiions:
I was aiming to write in manner as follows, but the result is not what I expected:
r1 = 10;
r2 = 20;
syms A B p2
eqn = [A-B/(r1^2)==0, A-B/(r2^2)==-p2];
Sol_A = solve(eqn,A)
Sol_B = solve(eqn,B)
It is clear that in the code above, the integration constants A, B are firstly solved so that they can be substituted into function . I would prefer to get directly in order to obtain an algorithm to use in other different problems, where the "solving by hand" is not so straightforward.
Thank you in advance

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Paul
Paul 2021-11-27
编辑:Paul 2021-11-27
syms sigma_r(r) A B p_2 r1 r2
sigma_r = A - B/r^2
sigma_r = 
% eqn = sigma_r == 0; % edit: commented out after posting original answer. Not used.
%r1 = 10; r2 = 20; % uncomment this line to get the solution directly
cond1 = subs(sigma_r,r,r1) == 0;
cond2 = subs(sigma_r,r,r2) == -p_2;
solAB = solve([cond1 cond2],[A B])
solAB = struct with fields:
A: (p_2*r2^2)/(r1^2 - r2^2) B: (p_2*r1^2*r2^2)/(r1^2 - r2^2)
sigma_r = subs(sigma_r,[A B],[solAB.A solAB.B])
sigma_r = 
sigma_r = subs(sigma_r,[r1 r2],[10 20])
sigma_r = 
  2 个评论
Richard
Richard 2021-11-27
编辑:Richard 2021-11-27
I really thank you for the effort. I am not a real expert in this branch, so I got stuck. By the way if I am not mistaken eqn = sigma_r == 0; is useless in this case.
Thank you again!
Paul
Paul 2021-11-27
You're not mistaken. I had defined eqn before I fully understood the question and then did not delete. I'll edit the post.

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