Abstract
The paper discusses the development of a method for constructing asymptotic formulas as \(x\to \infty\) for the fundamental solution system of two-termsingular symmetric differential equations of odd order with coefficients in a broad class offunctions that allow oscillation (with relaxed regularity conditions that do not satisfy the classicalTitchmarsh–Levitan regularity conditions). Using the example of a third-order binomial equation \(({i}/{2})\bigl[(p(x)y^{\prime })^{\prime \prime }+(p(x)y^{\prime \prime })^{\prime }\bigr ]+q(x)y =\lambda y\) , the asymptotics of solutions inthe case of various behavior of the coefficients \(q(x)\) and \(h(x)=-1+{1}\big/{\sqrt {p(x)}}\) is studied. New asymptoticformulas are obtained for the case in which \(h(x) \notin L_1[1,\infty )\) .
