Solving a high-order linear differential equation by the sequential differentiation method

Abstract

When teaching mathematics, the requirements for mathematics education are changing due to the rapid
development of science and technology. These changes, which are occurring and will continue to happen in the
near future in the field of mathematics education in higher education, are based on the needs required for a graduate
of a higher education institution. This leads to the strengthening of the applied direction of the mathematical course
and the elevation of the level of fundamental mathematical training. The article discusses the method of differentiation
by sequence, which is undoubtedly interesting for developing students’ creative abilities. In particular, it considers the
second-order differential equation whose solution is not an elementary function and can be presented in the form of a
series, thus yielding a new transcendental function. Using the method discussed here, it is possible to solve any order
differential equation. However, it is advisable to use it only when it is known in advance that the solution of the
equation exists in the form of a series. This method is mainly utilized in engineering practice and in research works
where the solution of the differential equation can be tested experimentally.