Keyword: «duhamel's formula»

The paper considers a brief theoretical information related to the application of operational calculus. The authors tabulate originals and images, basic theorems and models for the location of the image for the original; describe the ways to restore the original according to the known image. Since the classical methods of solutions of the Cauchy problem for linear differential equations with constant coefficients and right-hand side in the form of a composite function are highly intensive, clearly shows the efficiency of application of operational calculus and solutions of such problems. The parsed solution of the Cauchy problem for the Duhamel formula.