Trying to Solve system of 2 Equations "Unable to find explicit solution" Code In Description

Question

Michael Meyne 2023-11-4

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2042992-trying-to-solve-system-of-2-equations-unable-to-find-explicit-solution-code-in-description

评论： Walter Roberson 2023-11-6

采纳的回答： Walter Roberson

在 MATLAB Online 中打开

Code pasted below, thanks in advance:

clear all;

close all;

clc;

% Solve System of Equations

syms a1 a2 a3 r_1 r_2 alpha E

a3 = (alpha*E)/(8*pi);

[sol_a1, sol_a2] = solve(2*a3*log(r_1) + (a1/(r_1)^2) + a3 + 2*a2 == 0,...

2*a3*log(r_2) + (a1/(r_2)^2) + a3 + 2*a2 == 0);

Warning: Unable to find explicit solution. For options, see help.

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Answer 1

Walter Roberson 2023-11-4

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2042992-trying-to-solve-system-of-2-equations-unable-to-find-explicit-solution-code-in-description#answer_1346687

在 MATLAB Online 中打开

syms a1 a2 a3 r_1 r_2 alpha E

a3 = (alpha*E)/(8*pi);

eqn = [2*a3*log(r_1) + (a1/(r_1)^2) + a3 + 2*a2 == 0,...

2*a3*log(r_2) + (a1/(r_2)^2) + a3 + 2*a2 == 0];

partial_1 = solve(eqn(1), a1)

partial_1 =

eqn2 = subs(eqn(2:end), a1, partial_1)

eqn2 =

partial_2 = solve(eqn2(1), a2)

partial_2 =

sol_a2 = partial_2

sol_a2 =

sol_a1 = subs(partial_1, a2, sol_a2)

sol_a1 =

%cross-check

subs(eqn, {a1, a2}, {sol_a1, sol_a2})

ans =

isAlways(ans)

ans = 1×2 logical array

1 1

%or... more directly...

syms a1 a2 a3 r_1 r_2 alpha E

a3 = (alpha*E)/(8*pi);

[sol_a1, sol_a2] = solve(2*a3*log(r_1) + (a1/(r_1)^2) + a3 + 2*a2 == 0,...

2*a3*log(r_2) + (a1/(r_2)^2) + a3 + 2*a2 == 0, [a1, a2])

sol_a1 =

sol_a2 =

simplify(sol_a1)

ans =

simplify(sol_a2)

ans =

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Michael Meyne 2023-11-5

I have a quick question, how do you get the solution to be printed with this formatting?

Walter Roberson 2023-11-6

@Michael Meyne

When you have a sym() or symfun() or symmatrix() expression, then that sort of formatting happens automatically if you are using LiveScript or MATLAB Online or MATLAB Answers. It does not happen if you are using the traditional command window (and there is no way to turn it on for the command window)

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Answer 2

Sulaymon Eshkabilov 2023-11-4

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2042992-trying-to-solve-system-of-2-equations-unable-to-find-explicit-solution-code-in-description#answer_1346692

编辑：Sulaymon Eshkabilov 2023-11-4

在 MATLAB Online 中打开

Note that you have six unknowns (a1, a2, r_1, r_2, alpha, E) an two equations. It is possible to get two solution type expressions using IgnoreAnalyticalConstraints option, e.g.:

syms a1 a2 r_1 r_2 alpha E

a3 = (alpha*E)/(8*pi);

SOLUTION = solve(2*a3*log(r_1) + (a1/(r_1)^2) + a3 + 2*a2 == 0,...

2*a3*log(r_2) + (a1/(r_2)^2) + a3 + 2*a2 == 0, "IgnoreAnalyticConstraints",true)

SOLUTION = struct with fields:

r_1: exp(-((E*alpha)/2 + 8*pi*a2)/(E*alpha))*exp(wrightOmega(log(-(8*pi*a1)/(E*alpha)) + (E*alpha + 16*pi*a2)/(E*alpha))/2) r_2: exp(-((E*alpha)/2 + 8*pi*a2)/(E*alpha))*exp(wrightOmega(log(-(8*pi*a1)/(E*alpha)) + (E*alpha + 16*pi*a2)/(E*alpha))/2)

r_1 = SOLUTION.r_1

r_1 =

r_2 = SOLUTION.r_2

r_2 =

a3 = (alpha*E)/(8*pi)

a3 =