# 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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### Accepted Answer

Paul
on 27 Nov 2021

Edited: Paul
on 27 Nov 2021

syms sigma_r(r) A B p_2 r1 r2

sigma_r = A - B/r^2

% 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])

sigma_r = subs(sigma_r,[A B],[solAB.A solAB.B])

sigma_r = subs(sigma_r,[r1 r2],[10 20])

##### 2 Comments

Paul
on 27 Nov 2021

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