The key objective of this manuscript is to present new results for solving non-constant coefficients ordinary differential equations using a new integral transform called Khalouta transform (KhT). This new integral transform was defined and developed by the author in 2023. The new results presented consist in finding general formulas of solutions for the non-constant coefficients ordinary differential equations. Various numerical examples are presented in order to show the efficiency of the obtained results. Numerical test results confirm that the KhT technique is very effective in obtaining the exact solution of linear differential problems.