Note on fundamental system of solutions to the differential equations (<i>D</i> ² − 2<i>Dα</i> + <i>α</i> ² ± <i>β</i> ²) <i>y</i> = 0

Abstract The article deals with the study of the existence of a fundamental system of solutions to the differential equations: ( D 2 − 2 Dα + α 2 + β 2 ) y = 0, ( D 2 − 2 Dα + α 2 − β 2 ) y = 0, which are created using higher derivatives of the appropriate functions which are solutions to these equations. Special attention is paid to the solution of the generalized Cauchy problem with initial conditions.