Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 124, pp. 1-3.

Title: Existence and uniqueness of a local solution for $x' = f(t,x)$
       using inverse functions
        
Author: Jeffrey T. Hoag (Providence College, Providence RI, USA)

Abstract:
 A condition on the function $f$ is given such that the scalar ordinary
 differential equation $x' = f(t,x)$ with initial condition
 $x(t_0) = x_0$ has a unique solution in a neighborhood of $t_0$.
 An example illustrates that this result can be used when other theorems
 which put conditions on the difference $f(t,x)-f(t,y)$  do not apply.

Submitted January 13, 2013. Published May 20, 2013.
Math Subject Classifications: 34A12.
Key Words: Existence; uniqueness; ordinary differential equation.