On the solvability of the initial value problem for a factorized degenerate second-order differential equation

For a degenerate differential equation of the second order that splits into linear factors, a general solution is found whose form depends on the sign of the coefficients at the first derivative. The solvability of the Cauchy problem with an initial condition at the degeneracy point is established. The asymptotics of the constructed solutions are determined. Examples are given.