Application of Two-Parameter Laplace-Type R-transform to Solve Linear Ordinary Differential Equations

There are thirty one-parameter Laplace-type integral transforms, however, two-parameter Laplace-type integral transforms are few. Hence, the objective in the paper is to introduce and apply a new two-parameter Laplace-type integral transform, called the R-transform, to solve linear ordinary differential equations. Linear ordinary differential equations with constant coefficients were solved by taking the inverse R-transform. Also, two important theorems about the R-transform were proved. The theorems furnish us with the essential results for applications. Computations were manually done and confirmed with Mathematica software.