Existance and uniqueness can be determined however.
First we need to put the function in the form
this is how the equation is given
Now if the above is continuous and its partial with repect to y is continuous on some rectangle containing you intial condition then it has a solution and it is unique.
The above is continous on all of
and its partial with repect to y is
is also continuous on all of .
This tells us that a solution both exists and is unique.