We present the most complete multiwavelength coverage of any dwarf nova outburst: simultaneous optical, Extreme Ultraviolet Explorer, and Rossi X-ray Timing Explorer observations of SS Cygni throughout a narrow asymmetric outburst. Our data show that the high-energy outburst begins in the X-ray waveband 0.9--1.4d after the beginning of the optical rise and 0.6d before the extreme-ultraviolet rise. The X-ray flux drops suddenly, immediately before the extreme-ultraviolet flux rise, supporting the view that both components arise in the boundary layer between the accretion disc and white dwarf surface. The early rise of the X-ray flux shows the propagation time of the outburst heating wave may have been previously overestimated. The transitions between X-ray and extreme-ultraviolet dominated emission are accompanied by intense variability in the X-ray flux, with timescales of minutes. As detailed by Mauche & Robinson, dwarf nova oscillations are detected throughout the extreme-ultraviolet outburst, but we find they are absent from the X-ray lightcurve. X-ray and extreme-ultraviolet luminosities imply accretion rates of 3e15g/s in quiescence, 1e16g/s when the boundary layer becomes optically thick, and ~1e18g/s at the peak of the outburst. The quiescent accretion rate is two and a half orders of magnitude higher than predicted by the standard disc instability model, and we suggest this may be because the inner accretion disc in SS Cyg is in a permanent outburst state.
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