Solve symbolic equation by comparing coefficients

Question

Jörn Froböse 2022-2-9

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https://ww2.mathworks.cn/matlabcentral/answers/1646665-solve-symbolic-equation-by-comparing-coefficients

评论： Jörn Froböse 2022-2-17

采纳的回答： Prachi Kulkarni

I have an equation like this:

, which I need to rearrange to this form:

.

Obviously, the above holds true

for

and

. However, I would like to do this automatically. How can d and e be found using Matlabs Symbolic Toolbox?

The following approach won't help, since the system isn't well defined.

syms a b c d e f x y z

eq = a*x + y*(b + c*z)==0;

target = x + y*(d + e*z)==0;

solve([eq target],[d e])

Any help would be appreciated!

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Highphi 2022-2-9

在 MATLAB Online 中打开

syms a b c d e f x y z

eq(a,b,c) = a*x + y*(b + c*z);

target(a,b,c,d,e) = x + y*(d + e*z);

eq2(a,b,c,d,e) = subs(eq, [b, c], [d*a, e*a])

eq2(a, b, c, d, e) =

simplify(eq2)

ans(a, b, c, d, e) =

D = solve(eq2 == 0, d)

D =

E = solve(eq2 == 0, e)

E =

not sure if that helps much but maybe it'll help you get closer to where you want to be. (I'm not totally positive what you're trying to do with it 😝 )

Jörn Froböse 2022-2-10

Hey Highphi, thank you for your suggestion. This would'nt be really helpful in my case, since I need coefficients d and e without any dependence on x, y and z. I kind of solved it now by "brute-forcing" and using subs.

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Answer 1

Prachi Kulkarni 2022-2-15

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https://ww2.mathworks.cn/matlabcentral/answers/1646665-solve-symbolic-equation-by-comparing-coefficients#answer_896580

编辑：Prachi Kulkarni 2022-2-15

在 MATLAB Online 中打开

Hi,

For a given example expression of the form a*x + y*(b + c*x), you can get the coefficients d and e of the reduced forms as follows.

syms x y z
eq = 2*x + y*(3 + 4*z); % input equation
[d,e] = reducedCoefficients(eq);
function [d,e] = reducedCoefficients(eq)
    coef = coeffs(eq);
    b = coef(1);
    c = coef(2);
    a = coef(3);
    
    d = double(b/a);
    e = double(c/a);
end

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Prachi Kulkarni 2022-2-17

在 MATLAB Online 中打开

Hi,

For the general case, you can get the coefficients d and e of the reduced form as follows.

syms a b c x y z
eq = a*x + y*(b + c*z);
coef = coeffs(eq,[x,y,z]);
b = coef(1);
c = coef(2);
a = coef(3);
d = b/a;
e = c/a;

For your specific case, you can get the coefficients lambda and gamma of the reduced form as follows.

syms eta a Q d2ydt2 y t
eq = 4*(eta.^2)*d2ydt2 + 1.5*a*(Q.^2)*(1+cos(t))*y + y;
coef = coeffs(eq,[d2ydt2,y,cos(t)]);
lambda = coef(1)/coef(3);
gamma = coef(2)/coef(3);