A thin, non-uniform rod of mass \(M\) and length \(L\) is pivoted at a frictionless axle at its top end (\(x = 0\)). The rod's linear mass density varies along its length according to \(\lambda(x) = \lambda_0 \left(\dfrac{x}{L}\right)\), where \(\lambda_0\) is a constant and \(x\) is the distance from the pivot. The rod is held at rest displaced by an angle \(\theta\) relative to the downward vertical and then released. What is the magnitude of the rod's initial angular acceleration \(\alpha\) immediately after it is released?