I believe you should have put this in the differential equation section of the forum, not calculus.
PM a moderator and get them to move your post.
In my opinion the terms dx and dy don't indicate differentials but finite differences [otherwise an expression like dx= .3 is meaningless...]. In that case writing in the equation...
(1)
... y + dy instead of y and x + dx instead of x You obtain...
(2)
... that allows You to find the solution...
Kind regards