|Title of the article||
ON SINGULAR SOLUTIONS OF CLAIRAUT EQUATIONS IN THE THEORY OF ORDINARY DIFFERENTIAL AND PARTIAL DERIVATIVE EQUATIONS
Zhidova Lyubov' Aleksandrovna, Candidate of pedagogical sciences, associate professor, sub-department of mathematical analysis, Tomsk State Pedagogical University (60 Kiyevskaya street, Tomsk, Russia), E-mail: email@example.com
Background. There is no problem in finding a general solution to the ordinary differential Clairaut equation. The corresponding procedure is described in details in the theory of ordinary differential equations. Except of general solution being the family of linear functions, special (singular) solutions for the ordinary differential Clairaut equation may exist for which are no general methods to find them. This is evidenced by a very meager list in the accessible scientific literature of the types of Clairaut equations for which special solutions can be explicitly constructed. Therefore, it seems as an actual task finding and studies special solutions to the Clairaut equations. Goal of the present paper is finding and studies of special solutions to the Clairaut equations in the theory of ordinary differential equations and of partial differential equations and setting relations among special solutions to the Clairaut equation in the theory of ordinary differential equations and of partial differential equations.
ordinary differential equations, partial derivative equations, Clairaut equations, singular solutions
1. Kamke E. Spravochnik po differentsial'nym uravneniyam v chastnykh proizvodnykh pervogo poryadka [First order partial differential equations handbook]. Moscow: Nauka, 1966, 260 p. [In Russian]
Дата обновления: 16.09.2020 13:45