We propose a method to obtain axisymmetric, dynamic solutions to the Einstein equations that can represent a radiating collapsing body in slow differential rotation. The method is a generalization of the semi-numeric approach developed but Herrera, Jimenez, & Ruggeri, in 1980, for the spherically symmetric case. Solutions are properly matched to the exterior Kerr-Vaidya metric, and the values of the physically relevant variables (density, pressure, fluid velocity, and energy flux) are obtained inside the matter distribution. As an example of the method, a model based on Schwarzschild interior homogeneous static solution is presented.