Inverse problem for differential equations of higher order with singularity (Q1901954)

For the differential equation \[ ly \equiv y^{(n)} + \sum^{n - 2}_{j = 0} \left( {\nu_j \over x^{n - j}} + q_j (x) \right) y^{(j)} = \lambda y, \quad x > 0 \] where \(\nu_j\) are complex numbers and \(q_j (x)\) are complex-valued functions, the author investigates the inverse problem of evaluation of the differential operator \(l\) from the Weyl matrix. He obtains the so-called main equation of the inverse problem, proves its solvability, and presents an algorithm for its solution.