New formula for solution of one class of linear differential equations of the second order with the variable coefficients
Exact solutions for linear and nonlinear differential equations play an important role
in theoretical and practical research. In particular many works have been devoted to
finding a formula for solving second order linear differential equations with variable
coefficients. In this paper we obtained the formula for the common solution of the
linear differential equation of the second order with the variable coefficients in the
more common case. We also obtained the new formula for the solution of the Cauchy
problem for the linear differential equation of the second order with the variable
coefficients.Examples illustrating the application of the obtained formula for solving
second-order linear differential equations are given.
Key words: The linear differential equation, the second order, the variable
coefficients,the new formula for the common solution, Cauchy problem, examples.
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