Complicated expansions of solutions to an ordinary differential equation

Power asymptotics of solutions whose coefficients are series in power of multiple logarithms of the independent variable in an ordinary differential equation. Power asymptotics can be extended in the form of power expansions, whose coefficients are polynomials in its logarithm. An infinite number of steps are required for determining the entire expansion as well as each expansion. However, the initial segments of expansions and the first few expanses can always be calculated after a finite number of steps.