Free vibration analysis of heterogeneous (functionally graded) and non-uniform (variable thickness) disks using plane elasticity results in a two-point boundary value problem. Spatially varying mechanical and thickness properties yield variable coefficient governing differential equations where obtaining closed-form solutions are not possible except for certain simple grading and thickness functions. This article uses complementary functions method as a novel approach to determine natural frequencies of functionally graded non-uniform disks. The validation and observation of converges are done using analytical and ANSYS results for a simple power law model uniform disk. The proposed solution method can be applied for disks with any continuous thickness and material grading functions.