On the boundedness of solution of the first order ordinary differential equation with involution

In the present paper, the initial value problem for the first order ordinary differential equation with involution is studied. We obtain equivalent initial value problem for the second order ordinary differential equations to the initial value problem for first order linear differential equations with involution. Theorem on stability estimates for the solution of the initial value problem for the first order ordinary linear differential equation with involution is proved. Theorem on existence and uniqueness of bounded solution of initial value problem for first order ordinary nonlinear differential equation with involution is proved. © 2021 Author(s).