https://doi.org/10.36719/2663-4619/109/150-155
Sima Pashayeva
Military Institute named after H. Aliyev
Candidate of Physical and Mathematical Sciences
sima.pasayeva@gmail.com
Saltanat Veysova
Military Institute named after H. Aliyev
Candidate of Physical and Mathematical Sciences
seltenet.veysova63@gmail.com
Existence of Special Solutions to Ordinary Differential Equations
Abstract
The existence of singular solutions, the uniqueness and continuability of a solution on a given interval of a differential equation, resolved and unresolved with respect to the derivative investigate in this article. The proof of the existence and uniqueness of a solution to an unresolved differential equation with respect to the derivative is given with a different approach ̶ using the existence theorem of implicit function. In addition to researched the existence and uniqueness of a local solution to a differential equation, the existence of a global solution and the continuability of this solution beyond the boundary of the segment were also studied.
It is shown that a non-continuable solution in a given region can be determined only on a certain interval, which is the maximum interval of existence of the solution.
Keywords: continuability of the solution, existence and uniqueness of the solution, Lipschitz condition, singular point, particular solution, discriminant curves