It looks like the differential equation is
Factorize the right side by grouping.
Now we can separate variables as
Integrate both sides.
You could go on to solve for 
explicitly as a function of 
, but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.
For this case we are going to define the original coordinates:
(x, y): original coordinates.
We apply the transformation:
(x, y) -------> (-x, y + k)
We have:
-x: reflection on the y axis.
y + k: translation k units up.
Answer:
The point was reflected over the y-axis and translated up.
