Geodesic
Solution of the matrix equation $AX-XB=C$
Matematičeskie zametki, Tome 19 (1976) no. 3, pp. 449-451 
V. E. Shestopal. Solution of the matrix equation $AX-XB=C$. Matematičeskie zametki, Tome 19 (1976) no. 3, pp. 449-451. http://geodesic.mathdoc.fr/item/MZM_1976_19_3_a13/
@article{MZM_1976_19_3_a13,
     author = {V. E. Shestopal},
     title = {Solution of the matrix equation $AX-XB=C$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {449--451},
     year = {1976},
     volume = {19},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_3_a13/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Under the assumption of existence and uniqueness of the solution of the matrix equation $AX-XB=C$ we obtain a finite expression for $X$.