Solve symbolic equation by comparing coefficients

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Jörn Froböse
Jörn Froböse 2022-2-9
评论： Jörn Froböse 2022-2-17
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!
  2 个评论
Highphi
Highphi 2022-2-9
Ran in:
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
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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Prachi Kulkarni
Prachi Kulkarni 2022-2-15
编辑：Prachi Kulkarni 2022-2-15
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
  4 个评论
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Prachi Kulkarni
Prachi Kulkarni 2022-2-17
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);

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