TY  - JOUR
T1  - New Analytical Method For Solution of Second Order Ordinary Differential Equations With Variable Coefficients
AU  - Pala, Yaşar
AU  - Kahya, Çağlar
PY  - 2022
DA  - December
DO  - 10.18185/erzifbed.1009661
JF  - Erzincan University Journal of Science and Technology
PB  - Erzincan Binali Yildirim University
WT  - DergiPark
SN  - 2149-4584
SP  - 757
EP  - 774
VL  - 15
IS  - 3
LA  - en
AB  - In this study, we propose four methods for the analytical solution of second order ordinary non-homogeneous differential equations with variable coefficients. In the first case, the method directly gives the solution in explicit or integral form. In the second method, the solution of the problem reduces to the solutions of adjoined second order ordinary differential equation of homogeneous type. As long as the analytical solution of two adjoined equations can be solved, the analytical solution can always be found. In the third method, the differential equation is transformed into Riccati equation. Riccati equation is solved by means of a method recently developed. In order to solve non-homogeneous differential equation, the fourth method is developed. The strategy is different but the solution is again based on the solution of Riccati equation.
KW  - Second order
KW  - differential equations
KW  - analytical method
KW  - Riccati equation
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UR  - https://doi.org/10.18185/erzifbed.1009661
L1  - https://dergipark.org.tr/en/download/article-file/2026823
ER  -