Abstract:
In this paper, for an Euler-type linear equation of order $n$, we indicate a change of variable and conditions for the coefficients under which the equation is reduced to an equation with constant coefficients. For a solution of the inhomogeneous equation, we construct an explicit integral representation depending on the roots of the characteristic equation.
Keywords:linear equation of Euler type, model equation, characteristic of equation, fundamental solution, determinant of Vandermonde type.