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As is known, the problems for the differential equations with continuouslychanging order of the derivatives are not considered completely. In this paperwe consider the initial and boundary value problems for this type of linearordinary differential equations with constant coefficients and obtain analyticrepresentations of solutions of these problems. It should be noted that thisarea is one of the less studied fields of modern mathematics and there are noteffective methods for the study of problems for such differential equations,just as we study the problem for partial differential equations, with both withadditive and a multiplicative derivatives. The method used here is based on aninvariant for the above mentioned derivative, i.e. on the functions that do notchange for the derivative of any real positive order.

Investigation of the solutions of the Cauchy problem and boundary-value  problems for the ordinary differential equations with continuously changing  order of the derivative