[en] The kinetic equation describing temporal evolution of the ultra-relativistic electrons' energy spectrum effected by synchrotron losses and turbulent acceleration is solved for the isotropic part of the electrons' distribution function. The original distribution is assumed to be given in the form of a power spectrum. Turbulence properties are stated by means of the turbulent acceleration coefficient depending on epsilon energy D(epsilon)=D₀epsilon³ which is related to the synchrotron losses coefficient b(epsilon)=b₀epsilon³ so that the isotropization of the distribution function is provided without essential acceleration of particles. The initial spectrum is conserved up to some values of time t and energy epsilon connected by inequality epsilonb₀t<=1 and transformed into another one with a different index γ=b₀/D₀-2 if epsilonD₀t>>1 and b₀>>D₀. Finally, are possible applications of the solution to description of processes in supernova shells and radio galaxies are discussed