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In e+e- collisions recorded using the CLEO II.V detector we have studied the Cabibbo suppressed decay of D0 ->pi+pi-pi0 with the initial flavor of the D0 tagged by the decay D*+ ->D0pi+. We use the Dalitz-plot analysis technique to measure the resonant substructure in this final state and observe \rho\pi and non-resonant contributions by fitting for their amplitudes and relative phases. We describe the pipi S-wave with a K-matrix formalism and limit this contribution to the rate to be<2.5% @95% confidence level, in contrast to the large rate observed in D+ ->pi+pi-pi+ decay. Using the amplitudes and phases from this analysis, we calculate an integrated CP asymmetry of 0.01^{+0.09}_{-0.07} +/- 0.05.

Searches for CP Violation and \pi\pi S-Wave in the Dalitz-Plot Analysis of D0 -->\pi+\pi-\pi0