How I can solve AX+XB=0

Hello, How I am able to solve the expression AX+XB=0, where A and B are known 2x2 non-singular matrices and have to find X such that X = [x11 x12;x21 x22]. As far as I understand it is form of Sylvester Equation but by applying methods to solve it my only solution is zero but I want to reach at my expected solution.

Best Regards, SMK

Answer 1

[Azzi Abdelmalek]

Your equation can be written as

C*x=0 with a column vector x=[x11;x12;x21;x222]

Answer 2

[Taalaybek Akunov]

 belong to Ker(C). You can use (U,S,V)=svd(C) and then find V(:,i) corresponding to zero singular values in matrix S (for example, last singular value)