This work is committed to find the analytical solution of the versatile Sturm-Liouville equation with variable coefficients by kernelization approach. The introduced generated reproducing kernel Hilbert space (RKHS) structure is subjugated to represent the solution of such problems over the suggested kernel Hilbert space. The advancement of the suggested kernel is built on the matrix structure of the Strum-Liouville operator and the Gram-Schmidt orthogonalization to construct an orthonormal sequences in an inner product Hilbert space. We exhibit the legitimacy of the formalized reproducing kernel Hilbert space to the reckoned Sturm-Liouville differential equation with variable coefficients. Uniform convergence of the approximated solution retaining the recommended scheme is surveyed. The envisaged RHKS, the deployed Sturm-Liouville operator and the analytical solution of the aimed problem are instituted to show the recital of the recommended scheme.