Analytical solutions of the Rayleigh equation for empty and gas--filled bubble

The Rayleigh equation for bubble dynamics is widely used. However, analytical solutions of this equation have not been obtained previously. Here we find closed–form general solutions of the Rayleigh equation both for an empty and gas–filled spherical bubble. We present an approach allowing us to construct exact solutions of the Rayleigh equation. We show that our solutions are useful for testing numerical algorithms.