To construct the rotation curve of the Galaxy, classical Cepheids with proper motions, parallaxes and line-of-sight velocities from the Gaia DR2 Catalog are used in large part. The working sample formed from literature data contains about 800 Cepheids with estimates of their age. We determined that the linear rotation velocity of the Galaxy at a solar distance is $V_0=240pm3$~km s$^{-1}$. In this case, the distance from the Sun to the axis of rotation of the Galaxy is found to be $R_0=8.27pm0.10$~kpc. A spectral analysis of radial and residual tangential velocities of Cepheids younger than 120 Myr showed close estimates of the parameters of the spiral density wave obtained from data both at present time and in the past. So, the value of the wavelength $lambda_{R,theta}$ is in the range of [2.4--3.0] kpc, the pitch angle $i_{R,theta}$ is in the range of [$-13^circ$,$-10^circ$] for a four-arm pattern model, the amplitudes of the radial and tangential perturbations are $f_Rsim12$~km s$^{-1}$ and $f_thetasim9$~km s$^{-1}$, respectively. Velocities of Cepheids older than 120 Myr are currently giving a wavelength $lambda_{R,theta}sim5$~kpc. This value differs significantly from one that we obtained from the samples of young Cepheids. An analysis of positions and velocities of old Cepheids, calculated by integrating their orbits backward in time, made it possible to determine significantly more reliable values of the parameters of the spiral density wave: wavelength $lambda_{R,theta}=2.7$~kpc, amplitudes of radial and tangential perturbations are $f_R=7.9$~km s$^{-1}$ and $f_theta=5$~km s$^{-1}$, respectively.
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