On solution of pseudohyperbolic equation with constant coefficients

Thepaperproposesthemethodofformingtheexactsolutionofthefirstinitialboundaryvalueproblemforone-dimensionallinearpseudohyperbolicequation with constant coefficients. Toobtainthesolutiontype, themodificationofpartitionmethod (Fourier method) is used, when the type of one of the solution functional factors is consideredto be known. Atthesametime, theinitialproblemisreducedto parameterized family of Cauchy problems for ordinary differential equations. Thepaperpresentsexplicitly calculated formulas, whichspecify the solution. The qualitative research of the solution properties has been conducted. Theconditionsforcoefficientsintheformofinequalitieshave been obtained that is indicative ofboundedness and variability of the solutions. Several examples confirming the results obtained have been considered.