The time evolution of a disk crystal of ice with radius R and thickness h growing from supercooled water is studied using a solution of an ordinary differential equation (ODE) for h with respect to R. The growth of thickness, i.e., growth along the c axis of ice, is governed by slow molecular rearrangements on the basal plane and is expressed as a power function of the supercooling at the center of a disk face. Growth of the radius, i.e., growth in the basal plane, is controlled by transport of latent heat and is calculated by solving the diffusion equation for the temperature field surrounding the disk. We combine both functional expressions for growth rate to obtain an ODE for h as a function of. Our analysis in the (R, h) plane is used to understand the recent results obtained experimentally by Shimada and Furukawa (J. Phys. Chem. 1997, B101, 6171-6173), in which they found two types of growth, trajectories for ice disks prior to morphological instability.