In both theoretical and practical research, exact solutions for linear and nonlinear differential equations are crucial. Many studies have focused on discovering a formula for solving second order linear differential equations with variable coefficients. We found the formula for the common solution of the second-order linear differential equation with variable coefficients in the more common case in this study. We also discovered a new formula for solving the Cauchy problem for a second-order linear differential equation with variable coefficients. Examples of how to use the resulting formula to solve secondorder linear differential equations are provided.
Kyrgyz‐Turkish Manas University, Bishkek, Kyrgyzstan.
Institute of Mathematics, National Academy of Sciences of Kyrgyz Republic, Bishkek, Kyrgyzstan.
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